不等式
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056742549.png)
解集為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056757400.png)
,不等式
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056773673.png)
解集為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056789357.png)
,不等式
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056820788.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056835482.png)
解集為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056851289.png)
.
(1)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056867560.png)
;
(2)若“
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056867560.png)
”是“
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056851289.png)
”的充分條件,求實(shí)數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056913283.png)
的取值范圍.
(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056945663.png)
;(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056960526.png)
試題分析:(1)先解一元二次不等式求出集合M、N,然后即可求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056867560.png)
.
(2)由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056820788.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056835482.png)
可得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034057023764.png)
,因?yàn)椤?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056867560.png" style="vertical-align:middle;" />”是“
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056851289.png)
”的充分條件,所以集合
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056867560.png)
是集合
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056851289.png)
的子集,然后利用集合知識(shí)即可解決.
試題解析:(1)∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034057101594.png)
,∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034057116853.png)
. 2分
∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056773673.png)
,∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034057147674.png)
或
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034057179476.png)
. 4分
∴實(shí)數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056867560.png)
為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056945663.png)
.5分
(2)由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034057225739.png)
得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034057241771.png)
,
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034057257398.png)
,∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034057023764.png)
, 7分
又“
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056867560.png)
”是“
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056851289.png)
”的充分條件,∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034057335765.png)
. 9分
∴實(shí)數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056913283.png)
的取值范圍
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824034056960526.png)
. 12分
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