【题文】(本题10分)已知集合,,若,求实数、的值.
题型:难度:来源:
【题文】(本题10分)已知集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135402-96296.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135403-38342.png)
,若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135403-80019.png)
,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135403-36361.png)
、
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135404-36993.png)
的值.
答案
【答案】
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135404-49158.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135404-13254.png)
解析
【解析】
试题分析:将
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135403-80019.png)
转化为
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135404-85062.png)
,然后根据集合相等定义建立方程组,注意集合中元素的无序性,解出实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135403-36361.png)
、
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135404-36993.png)
的值,但要检验集合中元素的互异性.
试题解析:
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135405-77826.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135405-60776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135405-83510.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135406-17593.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135406-86280.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135404-49158.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135404-13254.png)
经检验
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135406-86280.png)
不合题意,舍去,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135404-49158.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135404-13254.png)
.
考点:集合的运算与相等.
举一反三
【题文】(本题12分)已知集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135345-11529.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135345-38149.png)
.若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135346-64523.png)
,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135346-81945.png)
的取值范围.
【题文】(本题14分)设
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135325-47209.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135326-80196.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135326-97012.png)
.
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135326-28519.png)
,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135327-89699.png)
的值;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135327-76337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135328-34730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135328-35967.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135328-92009.png)
,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135327-89699.png)
的值;
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135329-51448.png)
,实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135327-89699.png)
的值.
【题文】若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135138-12375.png)
,则实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322135138-96089.png)
的取值集合是
.
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