高一简单不等式题

来源:百度知道 编辑:UC知道 时间:2024/06/16 00:33:52
关于实数x的不等式|x-0.5(a+1)^2|≤0.5(a-1)^2与x^2-3(a+1)x+2(3a+1)≤0的解集分别为A、B,求使A是B的子集的取值范围

x-0.5(a+1)^2|≤0.5(a-1)^2
-(a-1)^2/2<= x-(a+1)^2/2<=(a-1)^2/2
2a<=x<=a^2+1

x^2-3(a+1)x+2(3a+1)≤0
(x-2)[x-(3a+1)]<=0
当2<=3a+1时,要A是B的子集
2<=2a,3a+1>=a^2+1
所以 1<=a<=3
当3a+1<2时,要A属于B,
3a+1<=2a,2>=a^2+1
所以 a=-1
所以a的范围:a=-1或1<=a<=3

好久没读过高一了