题目内容
观察下面的运算,完成下列各题的解答.
①判断下列各式是否成立:
(√)
(√)
(√)
(√)
②根据①判断的结果,你能发现什么规律?请用含有自然数n的式子将你发现的规律表示出来,并注明n的取值范围.
③请说明你所发现式子的正确性.
解:①√;√;√;√
②由2
=
=
,
=
=
,
=
=
,故根据上述规律可知n
(n≥2),
③等式n
成立,
理由:n
=
=
=
,
故结论成立.
分析:(1)计算等式左右两边是否相等,然后做出判断.
(2)由2
=
=
,
=
=
,
=
=
,故根据上述规律可知n
,
(3)把两式平方,证明左边和右边相等.
点评:本题主要考查二次根式的化简的知识点,找出等式规律很重要.
②由2
![](http://thumb.1010pic.com/pic5/latex/14762.png)
![](http://thumb.1010pic.com/pic5/latex/246712.png)
![](http://thumb.1010pic.com/pic5/latex/246713.png)
![](http://thumb.1010pic.com/pic5/latex/246714.png)
![](http://thumb.1010pic.com/pic5/latex/246715.png)
![](http://thumb.1010pic.com/pic5/latex/246716.png)
![](http://thumb.1010pic.com/pic5/latex/338501.png)
![](http://thumb.1010pic.com/pic5/latex/338502.png)
![](http://thumb.1010pic.com/pic5/latex/338503.png)
![](http://thumb.1010pic.com/pic5/latex/246717.png)
③等式n
![](http://thumb.1010pic.com/pic5/latex/246717.png)
理由:n
![](http://thumb.1010pic.com/pic5/latex/246718.png)
![](http://thumb.1010pic.com/pic5/latex/210014.png)
![](http://thumb.1010pic.com/pic5/latex/246719.png)
![](http://thumb.1010pic.com/pic5/latex/210012.png)
故结论成立.
分析:(1)计算等式左右两边是否相等,然后做出判断.
(2)由2
![](http://thumb.1010pic.com/pic5/latex/14762.png)
![](http://thumb.1010pic.com/pic5/latex/246712.png)
![](http://thumb.1010pic.com/pic5/latex/246713.png)
![](http://thumb.1010pic.com/pic5/latex/246714.png)
![](http://thumb.1010pic.com/pic5/latex/246715.png)
![](http://thumb.1010pic.com/pic5/latex/246716.png)
![](http://thumb.1010pic.com/pic5/latex/338501.png)
![](http://thumb.1010pic.com/pic5/latex/338502.png)
![](http://thumb.1010pic.com/pic5/latex/338503.png)
![](http://thumb.1010pic.com/pic5/latex/246717.png)
(3)把两式平方,证明左边和右边相等.
点评:本题主要考查二次根式的化简的知识点,找出等式规律很重要.
![](http://thumb2018.1010pic.com/images/loading.gif)
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