A=｛2,4,a²-2a+3｝,B=｛a+1,a²-4a+2,a²-3a+4,a²-5a+3｝若A∩B=｛2,3｝求A∪B

题目

A=｛2,4,a²-2a+3｝,B=｛a+1,a²-4a+2,a²-3a+4,a²-5a+3｝若A∩B=｛2,3｝求A∪B

答案

∵A∩B={2,3}∴{2,3}⊂A即3∈A∴a²-2a+3=3,解得a=0或者a=2当a=0时,A={2,3,4},B={1,2,4,3},则A∩B={2,3,4}≠{2,3},故舍去当a=2时,A={2,3,4},B={3,-2,2,-3},则A∩B={2,3}∴A∪B={-3,-2,2,3,4}...