题目内容
已知A=
,B=
,C=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613116461.png)
(1)试分别比较A与B、B与C的大小(只要写出结果,不要求证明过程);
(2)根据(1)的比较结果,请推测出
与
(
)的大小,并加以证明.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613085387.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613100463.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613116461.png)
(1)试分别比较A与B、B与C的大小(只要写出结果,不要求证明过程);
(2)根据(1)的比较结果,请推测出
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613131473.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613147494.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613163668.png)
(1) A>B,B>C;(2)
>
,证明见解析
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613131473.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613147494.png)
试题分析:(1)比较两个数大大小常用方法有:1、作差比较,2、作商比较,3、平方法,4,分析法;本题中
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240546132251830.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240546132561651.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240546132723219.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613287435.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613319439.png)
试题解析:(1) A>B 3分 B>C 6分
(2) 推测结果为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613131473.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613147494.png)
法一(求差法):∵(
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613131473.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613147494.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613521755.png)
又∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240546135371297.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613553884.png)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613131473.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613147494.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613163668.png)
法二(综合法):∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613646790.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613163668.png)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613677619.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613693570.png)
又∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613709728.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613740748.png)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613131473.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613147494.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613163668.png)
法三(分析法):欲证
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613131473.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613147494.png)
只需证
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240546138492146.png)
即证
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613677619.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613693570.png)
只需证
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613646790.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613927561.png)
只需证
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613943496.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613958316.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613958316.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613131473.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613147494.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824054613163668.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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