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【323430】2023九年级数学上册 第21章 二次根式 二次根式的概念和性质课后练习一(含解析)(

时间:2025-01-16 18:33:39 作者: 字数:2703字
简介:


二次根式的概念和性质


重难点易错点辨析

题面:如果 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,则( )

Aa <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> B. a <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> C. a <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> D. a  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


金题精讲

题一:

题面:化简 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> a0 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 得(  )

A  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>    B  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>    C  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>   D  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


题二:

题面:设实数ab在数轴上对应的位置如图所示,化简  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +|a+b|的结果是(  )

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

A.-2a+b B.2a+b C.-b D. b


满分冲刺

题一:

题面:已知实数xy满足 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,则以xy的值为两边长的等腰三角形的周长是( )

A 20 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 16 B20 C16 D.以上答案均不对


题二:

题面:若ab,满足3 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +5 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =7,设S=2 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> -3 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,求S的最大 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 值和最小值.





题三:

题面:如图,矩形ABCD中,点EF分别是ABCD的中点,连 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>DEBF,分别取DEBF的中点MN,连接AMCNMN,若AB=2 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> BC=2 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,则图中阴影部分的面积为

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>



思维拓展

题面:若0x1,则 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 等于(  )

A  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>    B <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>    C 2x   D 2x













 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>


课后练 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 习详解

重难点易错点辨析

答案:B.

详解:由已知得2a﹣1≤0,从而得出a的取值范围即可.

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,∴2a﹣1≤0,解得a <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .故选B

金题精讲

题一:

答案:C

详解:对分子化简后约分即可: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> · <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> |a <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> | <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =-a <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

题二:

答案:D.

详解:根据数轴上ab的值得出ab的符号,a0b0a+b0,∴ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +|a+b|=-a+a+b=b

故选:D


满分冲刺

题一:

答案: B.

详解:根据非负数的意义列出关于xy的方程并求出xy的值,再根据x是腰长和底边长两种情况讨论求解:

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 得,x4=0y8=0,即x=4y=8.

1)若4是腰长,则三角形的三边长为:448,不能组成三角形;

2)若4是底 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 边长,则三角形的三边长为:488,能组成三角形,周长为4+8+8=20.

故选B.

题二:

答案:S最大值= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> S最小值= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

详解:∵3 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> +5 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =7
 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> = <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
S= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
S= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> + <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>
 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> 都是非负数,
S
最大值= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> S最小值= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>

题三:

答案:2 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .

详解 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> :△B <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> CN与△ADM全等,面积也相等;△AME与△CNF全等,面积也相等,DFNMBEMN的面积也相等,所以阴影部分的面积其实就是原矩形面积的一半. <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> ,即阴影部分的面积为 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> .


思维拓展

答案:D

详解:(x <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )24(x <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )2 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> (x <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )24(x <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> )2.又∵ 0x1

 x <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>0x <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a>0.故 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/412/" title="概念" class="c1" target="_blank">概念</a> <a href="/tags/896/" title="根式" class="c1" target="_blank">根式</a> =2x.


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