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【324035】2024八年级数学下册 专题1.2 二次根式的乘除(重点题专项讲练)(含解析)(新版)

时间:2025-01-15 21:32:32 作者: 字数:14740字
简介:


 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 专题1.2 二次根式的乘除


 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

【典例1【阅读材料】小明在学习二次根式后,发现一些含根号的式子可以写成另一个式子的平方,如3+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2.善于思考的小明进行了以下探索:若设a+b <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> m+n <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2m2+2n2+2mn <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (其中abmn均为整数),则有am2+2n2b2mn.这样小明就找到了一种把类似a+b <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的式子化为平方式的方法.请你仿照小明的方法探索并解决下列问题:

【问题解决】

1)若a+b <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> m+n <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2,当abmn均为整数时,则a  b  .(均用含mn的式子表示)

2)若x+4 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> m+n <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2,且xmn均为正整数,分别求出xmn的值.

【拓展延伸】

3)化简 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>   

Shape1 思路点拨】

1)根据完全平方公式将等式右边展开,然后分析求解;

2)根据完全平方公式将等式右边展开,然后列方程求解;

3)根据完全平方公式和二次根式的性质进行变形化简.

Shape2 解题过程】

解:(1)(m+n <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2m2+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> mn+5n2

a+b <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> m+n <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2,且abmn均为整数,

am2+5n2b2mn

故答案为:m2+5n22mn

2)(m+n <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2m2+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> mn+3n2

x+4 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> m+n <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

又∵xmn均为正整数,

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

m1n2x13m2n1x7

3)原式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

故答案为: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

1.(江夏区校级月考)二次根式: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,是最简二次根式的有(  )个.

A2 B3 C4 D5

【思路点拨】

根据最简二次根式的定义,同时满足①被开方数不含能开得尽方的因数,②被开方数不含分母,才是最简二次根式,进行选择即可.

【解题过程】

解: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的被开方数中含有分母,所以不是最简二次根式;

2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 符合最简二次根式的定义,所以它们是最简二次根式;

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,二次根式的被开方数中含有能开得尽方的因数和因式,所以它们不是最简二次根式;

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 分母中含有二次根式,所以不是最简二次根式;

综上所述,上述二次根式中,属于最简二次根式的个数是4个.

故选:C

2.(罗庄区二模)等式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 成立的条件是(  )

Ax≠2 Bx≥﹣2 Cx≥﹣2x≠2 Dx2

【思路点拨】

根据二次根式和分式有意义的条件列不等式组求解.

【解题过程】

解:由题意可得 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

解得:x2

故选:D

3.(海淀区校级期末)下列各式互为有理化因式的是(  )

A <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

C <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

【思路点拨】

根据有理化因式定义:如果两个含有二次根式的非零代数式相乘,它们的积不含有二次根式,就说这两个非零代数式互为有理化因式,结合各个选项中两个代数式特征作出判断即可.

【解题过程】

解:A. <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,因此 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 不是有理化因式,故选项A不符合题意;

B <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a,所以 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 是有理化因式,因此选项B符合题意;

C.( <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )( <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )=﹣( <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2,所以 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )不是有理化因式,因此选项C不符合题意;

D.(x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> y <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )•(x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> y <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )=(x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> y <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2,因此x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> y <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> y <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 不是有理化因式,所以选项D不符合题意;

故选:B

4.(顺义区期末)当m0时,化简二次根式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,结果正确的是(  )

A <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

【思路点拨】

根据题目的已知可知n0,然后进行计算即可.

【解题过程】

解:由题意得:

m0n0

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

故选:D

5.(宝山区校级月考)若a0,化简2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的结果是(  )

A.(2b﹣3a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B.(﹣2b﹣3a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C.(﹣2b+3a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D.(2b+3a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

【思路点拨】

根据绝对值的性质和二次根式的性质进行化简即可.

【解题过程】

解:∵a0ab3≥0

b≤0

原式=2|b| <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 3|a| <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2b <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 3a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (﹣2b+3a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

故选:C

6.(武穴市期中)化简2ab <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的结果为(  )

Ab2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> Bb2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C.﹣b2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D.﹣b2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

【思路点拨】

根据二次根式有意义的条件进行化简即可.

【解题过程】

解:当b0a0时,

原式=2ab <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

b•|b| <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

=﹣b2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

b0a0时,

原式=﹣2ab <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

=﹣bb <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

=﹣b2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

故选:C

7.(思明区校级期末)若a2021×2022﹣20212b1013×1008﹣1012×1007c <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,则abc的大小关系是(  )

Acba Bacb Cbac Dbca

【思路点拨】

先化简各式,然后再进行比较即可.

【解题过程】

解:a2021×2022﹣20212

2021×2022﹣2021

2021×1

2021

b1013×1008﹣1012×1007

=(1012+1)(1007+1)﹣1012×1007

1012×1007+1012+1007+1﹣1012×1007

1012+1007+1

2020

c <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2020 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2021

bca

故选:D

8.(鄞州区校级期末)已知﹣1a0,化简 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的结果为(  )

A2a B2a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

【思路点拨】

直接利用完全平方公式结合a的取值范围、二次根式的性质分别化简得出答案.

【解题过程】

解:∵﹣1a0

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

故选:D

9.(金安区校级期末)若xy0,则二次根式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 化简的结果为  

【思路点拨】

直接利用二次根式的性质化简得出答案.

【解题过程】

解:∵xy0

xy同号,

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 有意义,

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 0

y0,则x0

二次根式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 化简的结果为:x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

故答案为: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

10.(浦东新区校级月考)设 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a+b,其中a为正整数,0b1,则ab  

【思路点拨】

先把 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 化简求出a+b的值,再根据a为正整数,b01之间求出符合条件的a的值,求出对应的b的值,代入原式进行计算即可.

【解题过程】

解:∵ <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 5 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

a+b5 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 6+ <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1).

a为正整数,0b1

a6b <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1

ab6﹣ <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1)=7 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

故答案为:7 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

11.(宁波模拟)若 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,则x6+y6的值是  

【思路点拨】

根据题意可求出x2+y2x2y2,利用平方差公式可求得x4y4,(x2y2)(x4y4)=x6+y6x2y4y2x4,由此可得答案.

【解题过程】

解:由题意得:x2+y22 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4x2y22 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )=2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> x4y4=(x2+y2)(x2y2)=8 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

又(x2y2)(x4y4)=x6+y6x2y4y2x4

可得:x6+y632+x2y2x2+y2)=32+2×440

故答案为:40

12.(闵行区校级期中)已知x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> y <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,且19x2+123xy+19y21985,则正整数n的值为  

【思路点拨】

先将xy分母有理化化简为含n的代数式,可得x+y4n+2xy1,然后将xy1代入19x2+123xy+19y21985,结果化简为x2+y298,进而求解.

【解题过程】

解:∵x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 22n+1﹣2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

y <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 22n+1+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

x+y4n+2xy1

xy1代入19x2+123xy+19y2198519x2+123+19y21985

化简得x2+y298

x+y2x2+y2+2xy98+2100

x+y10

4n+210

解得n2

故答案为:2

13.(浙江自主招生)若某个正整数m满足 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,则m  

【思路点拨】

先把分母有理化,再裂项相加,中间可以抵消即可求解.

【解题过程】

解:∵ <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

方程左边 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

所以得 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

解得m15

故答案为:15

14.(宝山区校级月考)

1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ;(2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

【思路点拨】

1)利用二次根式的乘除法的法则以及二次根式的性质与化简对式子进行运算即可;

2)先把系数相乘再把被开方数相乘,被开方数中的多项式要分解因式,约分后在化成最简的形式.

【解题过程】

解:(1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2)原式=﹣9 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

=﹣6 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

=﹣3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> |a|

15.(饶平县校级期末)观察下列各式,发现规律:

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ;…

1)填空: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>    <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>   

2)计算(写出计算过程): <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

3)请用含自然数nn≥1)的代数式把你所发现的规律表示出来.

【思路点拨】

1)根据已知等式得出规律,写出所求结果即可;

2)利用二次根式性质计算得到结果即可;

3)归纳总结得到一般性规律,写出即可.

【解题过程】

解:(1)根据题意得: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 5 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 6 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

故答案为:5 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 6 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2015 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

3)归纳总结得: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> n+1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (自然数n≥1).

16.(渭滨区期末)(一)阅读下面内容:

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2

(二)计算:

1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> n为正整数).

3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

【思路点拨】

(二)(1)原式分母有理化即可得到结果;

2)归纳总结得到一般性规律,写出即可;

3)原式利用得出的规律计算即可得到结果.

【解题过程】

解:(二)(1)原式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

3)原式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 19

17.(梁平区期末)阅读下述材料:

我们在学习二次根式时,熟悉了分母有理化及其应用.其实,有一个类似的方法叫做“分子有理化”:

与分母有理化类似,分母和分子都乘以分子的有理化因式,从而消掉分子中的根式.比如: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

分子有理化可以用来比较某些二次根式的大小,也可以用来处理一些二次根式的最值问题.例如:比较 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的大小.可以先将它们分子有理化.如下: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

因为 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,所以 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

再例如:求y <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的最大值.做法如下:

解:由x+2≥0x﹣2≥0可知x≥2,而y <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

x2时,分母 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 有最小值2,所以y的最大值是2

解决下述问题:

1)比较3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 42 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的大小;

2)求y <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的最大值.

【思路点拨】

1)利用分母有理化得到3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,利用3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 42 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 可判断3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 42 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2)根据二次根式有意义的条件得到由1+x≥0x≥0,则x≥0,利用分母有理化得到y <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,由于x0时, <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 有最小值1,从而得到y的最大值.

【解题过程】

解:(1)∵3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 42 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 42 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2)由1+x≥0x≥0x≥0

y <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

x0时, <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 有最小值1

y的最大值为1

18.(遵化市期末)定义:若两个二次根式ab满足abc,且c是有理数,则称ab是关于c的共轭二次根式.

1)若a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 是关于4的共轭二次根式,则a  

2)若2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> m是关于2的共轭二次根式,求m的值.

【思路点拨】

1)根据共轭二次根式的定义列等式可得a的值;

2)根据共轭二次根式的定义列等式可得m的值.

【解题过程】

解:(1)∵a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 是关于4的共轭二次根式,

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a4

a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

故答案为:2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2)∵2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> m是关于2的共轭二次根式,

2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )(4 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> m)=2

4 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> m <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4﹣2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

m=﹣2

19.(南川区期中) <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 6+32 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 7+72 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

1)观察上面的式子,请你猜想a+b2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0b≥0)的大小关系,并说明理由;

2)请利用上述结论解决下面问题:如图,某同学在做一个面积为800cm2,对角线相互垂直的四边形风筝时,求用来做对角线的竹条至少要多少厘米?

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

【思路点拨】

1)参照题干例子可直接写出,可用完全平方公式来说明理由;

2)设对角线的长分别为a厘米,b厘米,则 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 800,再根据公式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 可得答案.

【解题过程】

解:(1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a≥0b≥0).理由如下:

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 0

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2)设对角线的长分别为a厘米,b厘米,由对角线互相垂直,四边形面积可表示为 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 800

ab1600

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 80

所以用来做对角线的竹条至少要用80cm

20.(饶平县校级期末)观察下列等式:回答问题:

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,…

1)根据上面三个等式的信息,猜想 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>   

2)请按照上式反应的规律,试写出用n表示的等式;

3)验证你的结果.

【思路点拨】

根据观察,可得规律: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

【解题过程】

解:(1)根据上面三个等式的信息,猜想 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

故答案为:1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

21.(龙口市期中)阅读下列解题过程

例:若代数式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值是2,求a的取值范围.

解:原式=|a﹣1|+|a﹣3|

a1时,原式=(1﹣a+3﹣a)=4﹣2a2,解得a1(舍去);

1≤a≤3时,原式=(a﹣1+3﹣a)=22,符合条件;

a3时,原式=(a﹣1+a﹣3)=2a﹣42,解得a3(舍去)

所以,a的取值范围是1≤a≤3

上述解题过程主要运用了分类讨论的方法,请你根据上述理解,解答下列问题

1)当2≤a≤5时,化简: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>   

2)若等式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4成立,则a的取值范围是  

3)若 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 8,求a的取值.

【思路点拨】

1)根据二次根式的性质即可求出答案;

2)先将等式的左边进行化简,然后分情况讨论即可求出答案;

3)先将等式的左边进行化简,然后分情况讨论即可求出答案;

【解题过程】

解:(1)∵2≤a≤5

a﹣2≥0a﹣5≤0

原式=|a﹣2|+|a﹣5|

a﹣2﹣a﹣5

3

2)由题意可知:|3﹣a|+|a﹣7|4

a≤3时,∴3﹣a≥0a﹣70

原方程化为:3﹣aa﹣7)=4

a3,符合题意;

3a7时,

3﹣a0a﹣70

∴﹣3﹣a)﹣(a﹣7)=4

44,故3a7符合题意;

a≥7时,

3﹣a0a﹣7≥0

∴﹣3﹣a+a﹣7)=4

a7,符合题意;

综上所述,3≤a≤7

3)原方程可化为:|a+1|+|a﹣5|8

a≤﹣1时,∴a+1≤0a﹣50

原方程化为:﹣a﹣1﹣a﹣5)=8

a=﹣2,符合题意;

当﹣1a5时,

a+10a﹣50

a+1)﹣(a﹣5)=8

此方程无解,故﹣1a5不符合题意;

a≥5时,

a+10a﹣5≥0

a+1+a﹣58

a6,符合题意;

综上所述,a=﹣2a6

故答案为:(13;(23≤a≤7

22.(漳浦县期中)阅读下面例题:化简 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

解:∵ <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2+572 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

7+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

由上述例题的方法化简:

1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

【思路点拨】

1)根据完全平方公式、二次根式的性质化简;

2)先把 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 变形,再根据完全平方公式、二次根式的性质化简;

3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> x,求出x2,再根据完全平方公式、二次根式的性质化简.

【解题过程】

解:(1)∵5﹣2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 3﹣2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=( <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2﹣2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2=( <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

3)设 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> x

x2=( <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2

4 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

8+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

8+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

8+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

8+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2

6+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1,即 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/153/" title="乘除" class="c1" target="_blank">乘除</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 1


1