题目内容


设集合A={x2,2x-1,-4},B={x-5,1-x,9},若AB={9},求AB.


解 由9∈A,可得x2=9或2x-1=9,

解得x=±3或x=5.

x=3时,A={9,5,-4},B={-2,-2,9},B中元素重复,故舍去;

x=-3时,A={9,-7,-4},B={-8,4,9},AB={9}满足题意,故AB={-7,-4,-8,4,9};

x=5时,A={25,9,-4},B={0,-4,9},

此时AB={-4,9}与AB={9}矛盾,故舍去.

综上所述,AB={-8,-4,4,-7,9}.


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