题目内容
已知关于x的不等式:
<1.
(1)当a=1时,解该不等式;
(2)当a>0时,解该不等式.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053038679.png)
(1)当a=1时,解该不等式;
(2)当a>0时,解该不等式.
(1){x|1<x<2}(2)a=2时,解集为
;0<a<2时,解集为
,a>2时,解集为![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053085834.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053054359.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053069820.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053085834.png)
(1)当a=1时,不等式化为
<1,化为
<0,
∴1<x<2,解集为{x|1<x<2}.
(2)a>0时,由
<1得
<0,
(ax-2)(x-1)<0,方程(ax-2)(x-1)=0的两根x1=
,x2=1.
①当
=1即a=2时,解集为
;
②当
>1即0<a<2时,解集为
;
③当
<1即a>2时,解集为![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053085834.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053085537.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053101468.png)
∴1<x<2,解集为{x|1<x<2}.
(2)a>0时,由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053038679.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053132541.png)
(ax-2)(x-1)<0,方程(ax-2)(x-1)=0的两根x1=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053147393.png)
①当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053147393.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053054359.png)
②当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053147393.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053069820.png)
③当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053147393.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824041053085834.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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