【题文】(本题满分12分)已知集合(1)当时,求; (2)当时,求
题型:难度:来源:
【题文】(本题满分12分)已知集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133625-61047.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133625-40325.png)
时,求
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133626-81367.png)
;
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133626-87913.png)
时,求使
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133626-69367.png)
的实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133626-35015.png)
的取值范围.
答案
【答案】(1)
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133627-67785.png)
;(2)
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133627-94926.png)
;
解析
【解析】
试题分析:(1)将a=2代入到集合A,集合B中,得到此时集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133628-71265.png)
,集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133628-26541.png)
,因此,集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133629-56245.png)
,集合B
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133629-94916.png)
,故
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133629-70440.png)
;(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133626-87913.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133630-13265.png)
,所以集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133630-82870.png)
,集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133630-23574.png)
,要是
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133626-69367.png)
,则集合B是集合A的子集,画出两个集合的区域,有
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133631-22697.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133631-16703.png)
,解出a的范围即可;
试题解析:(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133625-40325.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133629-56245.png)
2分
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133629-94916.png)
4分
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133629-70440.png)
6分
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133626-87913.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133630-13265.png)
7分
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133630-23574.png)
9分
∵
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133626-69367.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133632-42482.png)
11分
即
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133632-56333.png)
12分
考点:?不等式的求法?子集的概念
举一反三
【题文】(本小题满分10分)已知集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133524-35143.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133524-23868.png)
.
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133525-46226.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133525-15207.png)
;
(Ⅱ)已知
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133525-48453.png)
,若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133525-21867.png)
,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133526-10562.png)
的取值范围.
【题文】(本小题满分12分)已知方程
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133442-52658.png)
的两个不相等实根为
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133443-21147.png)
.集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133443-92013.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133443-62363.png)
{2,4,5,6},
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133445-73265.png)
{1,2,3,4},A∩C=A,A∩B=
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133445-41140.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322133446-48919.png)
的值.
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