题目内容
定义在
上的函数
,若关于
的
方程
,有3个不同实数解
,且
,则下列说法中正确的是:( )
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643625344.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643641231.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643282206.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643329881.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643360187.gif)
方程
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643360661.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643391393.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643407415.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643423202.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643438285.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643454209.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643469452.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643485205.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643501296.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643516212.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643625344.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643641231.gif)
D
有三个根,故必有一根是2,且其他两根必有一根小于2,一根大于2,
由
,可知![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643781241.gif)
当
时,
,代入可得
,所以![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643828277.gif)
不妨设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643875295.gif)
则方程
有唯一解(若
有两解,则对应的
有4个)
从而△=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643984921.gif)
所以
,从而
,此时方程变为
所以
,
即
=1,解得
,
,又
,所以![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643625344.gif)
,选D
由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643407415.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643781241.gif)
当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643797232.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643797312.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643828410.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643828277.gif)
不妨设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643844618.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643875295.gif)
则方程
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643937494.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643953185.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643360187.gif)
从而△=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643984921.gif)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135644000243.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135644203236.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135644218439.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135644249223.gif)
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135644296307.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135644312244.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135644327249.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643781241.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643625344.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135643641231.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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