已知命題
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823440289.png)
:復數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823456461.png)
,復數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240338234721560.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823550388.png)
是虛數(shù);命題
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823550333.png)
:關于
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823565266.png)
的方程
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823581955.png)
的兩根之差的絕對值小于
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823596291.png)
;若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823628467.png)
為真命題,求實數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823628337.png)
的取值范圍.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823628337.png)
的取值范圍為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823659875.png)
.
試題分析:對于
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823440289.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240338236901232.png)
為虛數(shù)的條件是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823706685.png)
且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823721471.png)
,然后將
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823628337.png)
的范圍求出來;對于
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823550333.png)
,利用二次方程根與系數(shù)的關系并結合不等式
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240338237681000.png)
求解出
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823628337.png)
的取值范圍;由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823628467.png)
為真命題可知,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823799417.png)
都為真命題,故求出
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823799417.png)
為真時的
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823628337.png)
的取值范圍的集合的交集即可.
試題解析:由題意知,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240338239241539.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240338239551091.png)
2分
若命題
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823440289.png)
為真,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823550388.png)
是虛數(shù),則有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823706685.png)
且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823721471.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823628337.png)
的取值范圍為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033824064434.png)
且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033824080459.png)
且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033824096712.png)
4分
若命題
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823550333.png)
為真,則有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240338241271943.png)
7分
而
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033824158986.png)
所以有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240338241741460.png)
或
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033824189660.png)
10分
由題意知,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033824205411.png)
都是真命題,實數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823628337.png)
的取值范圍為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824033823659875.png)
12分.
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