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【324039】2024八年级数学下册 专题1.3 二次根式的混合运算与化简求值(重点题专项讲练)(含

时间:2025-01-15 21:33:04 作者: 字数:12916字
简介:


 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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1.3 二次根式的混合运算与化简求值


 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,求 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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.

Shape1 思路点拨】

先根据 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 求出x的值,表示出(x+2)与(x2+4x)的值,再把原式进行化简,代入即可求出原式的值.

Shape2 解题过程】

解:∵ <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

xa <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

x+2a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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+4xxx+4)=(a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 4a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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≥0

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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≥1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

原式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 时,

原式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a2

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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.(广西月考)在二次根式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 中与 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 是同类二次根式的有(  )

A1 B2 C3 D4

【思路点拨】

将二次根式进行化简,然后根据同类二次根式的概念进行判断.

【解题过程】

解: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 是同类二次根式,共2个,

故选:B

2.(平房区期末)若最简二次根式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 能合并,则ab的值分别是(  )

A21 B12 C22 D11

【思路点拨】

根据题意得到两个二次根式是同类二次根式,列出方程组,求出方程组的解即可得到ab的值.

【解题过程】

解:∵最简二次根式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 能合并,

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,即 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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得:7a7

解得:a1

a1代入②得:1+2b3

解得:b1

故选:D

3.(浦东新区校级期中)设xy都是负数,则 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 等于(  )

A <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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xy都是负数,可以将所求式子变形,然后即可化简题目中的式子,本题得以解决.

【解题过程】

解:∵xy都是负数,

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

故选:D

4.(南召县期末)用※定义一种新运算:对于任意实数mn,规定mnm2nmn﹣3n,如:1※212×2﹣1×2﹣3×2=﹣6.则(﹣2)※ <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 结果为(  )

A <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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】

根据定义新运算法则列式,然后先算乘方和乘法,再算加减.

【解题过程】

解:原式=(﹣22 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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:A

5.(遵化市模拟)在一个大正方形上,按如图的方式粘贴面积分别为1210的两个小正方形,粘贴后,这两个小正方形重合部分的面积为3,则空白部分的面积为(  )

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

A8 B19 C6 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

【思路点拨】

根据题意求出两个小正方形的边长,可得出大正方形的边长,进而得出答案.

【解题过程】

解:∵两个小正方形面积分别为1210

两个小正方形的边长分别为2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

两个小正方形重合部分的边长为2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 大正方形的边长,

两个小正方形的重合部分是正方形,

两个小正方形重合部分的面积为3

重合部分的边长为 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

大正方形的边长是2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

空白部分的面积为( <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 212+10﹣3)=2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

故选:D

6.(九龙坡区校级月考)已知x+y=﹣5xy4,则 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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(  )

A <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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】

根据已知条件得出xy同号,并且xy都是负数,求出x=﹣1y=﹣4x=﹣4y=﹣1,再求出答案即可.

【解题过程】

解:∵x+y=﹣5xy4

xy同号,并且xy都是负数,

解得:x=﹣1y=﹣4x=﹣4y=﹣1

x=﹣1y=﹣4时, <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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=﹣4y=﹣1时, <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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:B

7.(海淀区校级期末)已知xy为实数,xy5,那么x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值为(  )

A <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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±2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D5

【思路点拨】

先化简所求式子,然后利用分类讨论的方法,可以求得所求式子的值.

【解题过程】

解:x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

xy为实数,xy5

xy同号,

x0y0时,

原式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

x0y0时,

原式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

由上可得,x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

8.(武昌区校级自主招生)已知x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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x6﹣2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> x5x4+x3﹣2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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+2x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 的值为(  )

A0 B1 C <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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】

对已知进行变形,再代入所求式子,反复代入即可.

【解题过程】

解:∵x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

x6﹣2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> x5x4+x3﹣2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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+2x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

x5x﹣2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )﹣x4+x2x﹣2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

x5 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )﹣x4+x2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

x5 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )﹣x4+x2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

x4[x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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]+x2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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+x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +2x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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+2x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

9.(宽城县期末)(1)计算: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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)下面是王鑫同学进行实数运算的过程,认真阅读并完成相应的问题:

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 第一步

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 第二步

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 第三步

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 第四步

以上化简步骤中第一步化简的依据是:  

  步开始出现错误,请写出错误的原因  ,该运算正确结果应是  

【思路点拨】

1)利用平方差公式计算;

2)先把各二次根式化简,然后合并即可;

3)①第一步化简的依据为二次根式的除法法则;

第二步去括号错误,然后计算出正确的结果.

【解题过程】

解:(1)原式=5﹣3+13

2)原式=5 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 9 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

5 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

5 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

3)①化简步骤中第一步化简的依据是商的算术平方根,等于算术平方根的商;

故答案为:商的算术平方根,等于算术平方根的商;

第二步开始出现错误,请写出错误的原因括号前是负号,去掉括号后第二项没有变号;,该运算正确结果应是 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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:二;括号前是负号,去掉括号后第二项没有变号; <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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)先化简,再求值:[ <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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x3y2

【思路点拨】

根据二次根式的化简求值即可求解.

【解题过程】

解:原式=( <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

x3y2时,

原式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

答:原式的值为 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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.(杭州模拟)最简根式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 能是同类根式吗?若能,求出xy的值;若不能,请说明理由.

【思路点拨】

根据同类根式的定义,即可推出 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 2xy <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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+6),x+y3x+y﹣2,通过解二元一次方程组即可推出xy的值.

【解题过程】

解:假设他们是同类根式,则: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 时,x+y=﹣13x+y﹣2=﹣1

两根式皆无意义,

假设错误,它们不能是同类根式.

12.(浦东新区校级月考)已知x3+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,求: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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.

【思路点拨】

利用完全平方公式把原式变形,根据二次根式的除法法则求出 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,代入计算即可.

【解题过程】

解:原式=x2+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 6x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

=(x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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+6x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

=(x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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)(x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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),

x3+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

原式=(6+1×6+5)=77

13.(雨花区校级期末)已知x3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> y3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,求下列各式的值:

1x2+y2

2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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)根据完全平方公式对原式进行变形,然后利用二次根式加减法和平方差公式求得x+yxy的值,从而代入求值;

2)原式进行通分计算,然后利用整体思想代入求值.

【解题过程】

解:(1)原式=(x+y2﹣2xy

x3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> y3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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+y=(3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

xy=(3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )=9﹣72

原式=62﹣2×2

36﹣4

32

2)原式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

xy2x2+y232时,

原式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 16

14.(思明区校级期中)阅读材料:

如果一个三角形的三边长分别为abc,记p <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,那么这个三角形的面积S <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .这个公式叫“海伦公式”,它是利用三角形三条边的边长直接求三角形面积的公式.中国的秦九韶也得出了类似的公式,称三斜求积术,故这个公式又被称为“海伦秦﹣﹣﹣九韶公式”完成下列问题:

如图,在△ABC中,a7b5c6

1)求△ABC的面积;

2)设AB边上的高为h1AC边上的高为h2,求h1+h2的值.

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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)根据题意先求p,再将pabc的值代入题中所列面积公式计算即可;

2)按照三角形的面积等于 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ×高分别计算出h1h2的值,再求和即可.

【解题过程】

解.(1)根据题意知p <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 9

所以S <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

∴△ABC的面积为6 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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)∵S <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ch1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> bh26 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 6h1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 5h26 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

h12 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> h2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

h1+h2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

15.(郫都区期末)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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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:

a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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=(m <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> n2(其中abmn均为正整数),则有a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> bm2+2n2+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

am2+2n2b2mn.这样小明就找到了一种把部分a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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:

1)当abmn均为正整数时,若a <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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=(m <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> n2,用含mn的式子分别表示ab,得:a  b  

2)若a+4 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> n2,且amn均为正整数,求a的值;

3)化简: <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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)利用完全平方公式展开得到(m <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> n2m2+6n2+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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,从而可用mn表示ab

2)直接利用完全平方公式,变形得出答案;

3)直接利用完全平方公式,变形化简即可.

【解题过程】

解:(1)∵(m <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> n2m2+6n2+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> mna <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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=(m <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> n2

am2+6n2b2mn

故答案为m2+6n22mn

2)∵(m <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> n2m2+3n2+2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> mna+4 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> n2

am2+3n2mn2

mn均为正整数,

m1n2m2n1

a137

3 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

16.(渝中区校级月考)先阅读,再解答问题:恒等变形,是代数式求值的一个很重要的方法.利用恒等变形,可以把无理数运算转化为有理数运算,可以把次数较高的代数式转化为次数较低的代数式.

例如:当x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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时,求 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> x3x2x+2的值.

为解答这道题,若直接把x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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代入所求的式中,进行计算,显然很麻烦,我们可以通过恒等变形,对本题进行解答.

方法:将条件变形,因x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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,得x﹣1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,再把等式两边同时平方,把无理数运算转化为有理数运算.

x﹣1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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x2﹣2x﹣20,即x2﹣2x2x22x+2

原式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> x2x+2)﹣x2x+2x2+xx2x+22

请参照以上的解决问题的思路和方法,解决以下问题:

1)若x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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,求2x3+4x2﹣3x+1的值;

2)已知x2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,求 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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.

【思路点拨】

1)变形已知条件得到x+1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,两边平方得到x2+2x1,再利用降次和整体代入的方法表示原式化为﹣x+1,然后把x的值代入计算即可;

2)变形已知条件,利用平方的形式得到x2﹣4x=﹣1x24x﹣1,再利用降次和整体代入的方法化简原式,从而得到原式的值.

【解题过程】

解:(1)∵x <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

x+1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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+122

x2+2x+12

x2+2x1

原式=2xx2+2x)﹣3x+1

2x﹣3x+1

=﹣x+1

=﹣( <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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

2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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)∵x2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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﹣2 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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﹣223

x2﹣4x+43

x2﹣4x=﹣1x24x﹣1

原式 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 16x2﹣8x+1﹣4x2+x﹣36x+9﹣5x+5

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> [124x﹣1)﹣48x+15

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 48x﹣12﹣48x+15

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

17.(成都期中)阅读材料:善于思考的小军在解方程组 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 时,采用了一种“整体代换”的解法:

解:将第二个方程,变形为4x+10y+y5,即22x+5y+y5

然后把第一个方程,代入得2×3+y5,∴y=﹣1

y=﹣1代入第一个方程,得x4

方程组的解为 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

请你解决下列两个问题:

1)模仿小军的“整体代换”法解方程组 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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)已知正数xy满足 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,求 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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.

【思路点拨】

1)把第2个方程变形为33x﹣2y+2y19,则利用整体代换消去x,求出y的值,然后利用代入法求出x得到方程组的解;

2)利用整体代换的方法把原方程组转化为方程组 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,再利用完全平方公式得到( <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,然后利用整体代入的方法计算.

【解题过程】

解:(1 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

把②变形为9x﹣6y+2y19,即33x﹣2y+2y19③

把①代入③,得3×5+2y19

y2

y2代入①,得3x﹣2×25

x3

方程组的解为 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

把①变形为3x2+1.5xy+12y2﹣3.5xy47,即1.52x2+xy+8y2)﹣3.5xy47③

把②代入①,得1.5×36﹣3.5xy47

xy2

xy2代入②,得2x2+2+8y236

x2+4y217

x2+4xy+4y217+8

即(x+2y225

x0y0

x+2y5

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

18.(浙江自主招生)已知正实数xyz满足方程组 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 求该方程组的所有实数解.

【思路点拨】

xy,根据二次根式的性质和分母有理化的知识进行化简即可.

【解题过程】

解:不妨令xy,有 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,得 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

zx

zy

 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,得 <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

yx

yx

xyz,代入解得:xyz <a href="/tags/36/" title="重点" class="c1" target="_blank">重点</a> <a href="/tags/45/" title="混合" class="c1" target="_blank">混合</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/282/" 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