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问题: 范围

若A=[2a,a^2+1],B={x|x^2-3(a+1)+2(3a+1)≤0},求使A包含于B时a的取值范围.

解答:

A包含于B,B是子集,
x^2-3(a+1)+2(3a+1)≤0,
(x-2)(x-3a-1)<0
2<3a+1时,2<2a<a^2+1<3a+1,得1<a<3
3a+1<2时,3a+1<2a<a^2+1<2,无解
a的取值范围(1,3)