试题与答案

已知A={x|a≤x≤2a+3},B={x|x2+5x﹣6>0}. (Ⅰ)若A∩

题型:解答题

题目:

已知A={x|a≤x≤2a+3},B={x|x2+5x﹣6>0}.

(Ⅰ)若A∩B={x|1<x≤3},求a的值;

(Ⅱ)若A∪B=B,求a的取值范围.

答案:

解:∵A={x|a≤x≤2a+3},B={x|x2+5x﹣6>0}=[x|x<﹣6,或x>1}.

(Ⅰ)依题意A∩B={x|1<x≤3}可得  

∴a=0.

(Ⅱ)由A∪B=B得AB.

①当A=时满足题意,此时,a>2a+3,解得a<﹣3.

②当A≠时,,解得 a>1.

综上,a的取值范围为:a<﹣3 或 a>1,即 (﹣∞,﹣3)∪(1,+∞).

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