已知集合U={0,1,2,3},A={x∈U|x2+mx=0},(1)若?UA={1,2},求实数m的值;(2)若集合A是单元素集(

2025-05-19 01:20:55
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回答(1):

(1)∵集合U={0,1,2,3},A={x∈U|x2+mx=0},?UA={1,2},
∴A={0,3},
由A中方程变形得:x(x+m)=0,
解得:x=0或x=-m,
可得-m=3,
解得:m=-3;
(2)∵A是单元素集,
∴A中方程△=0,即m2=0,
解得:m=0.