题目内容
若a、b为任意实数,下列式子一定成立的是( )A.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103000036008129206/SYS201311030000360081292006_ST/0.png)
B.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103000036008129206/SYS201311030000360081292006_ST/1.png)
C.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103000036008129206/SYS201311030000360081292006_ST/2.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103000036008129206/SYS201311030000360081292006_ST/3.png)
D.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103000036008129206/SYS201311030000360081292006_ST/4.png)
【答案】分析:根据二次根式的运算法则进行计算即可.
解答:解:A、原式=
=|a-b|,不一定成立;
B、
=a2,一定成立;
C、a>0,b>0时,
=
•
,a<0,b<0时原式不成立;
D、原式在a>0,b>0时成立,a<0,b<0时原式不成立.
故本题选B.
点评:正确理解二次根式乘法、积的算术平方根等概念是解答问题的关键.需注意二次根式的双重非负性:a≥0,
≥0.
解答:解:A、原式=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103000036008129206/SYS201311030000360081292006_DA/0.png)
B、
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103000036008129206/SYS201311030000360081292006_DA/1.png)
C、a>0,b>0时,
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103000036008129206/SYS201311030000360081292006_DA/2.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103000036008129206/SYS201311030000360081292006_DA/3.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103000036008129206/SYS201311030000360081292006_DA/4.png)
D、原式在a>0,b>0时成立,a<0,b<0时原式不成立.
故本题选B.
点评:正确理解二次根式乘法、积的算术平方根等概念是解答问题的关键.需注意二次根式的双重非负性:a≥0,
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103000036008129206/SYS201311030000360081292006_DA/5.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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