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

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/19 19:19:35
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

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
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

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
∵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}

这个A∩B={2,3}说明AB中均含有2,3
所以,A中的a^2-2a+3=3,a=0或2
若a=0,那么B中的1,2,3,4那满足A∩B={2,3,4}不合题意舍去
所以,a=2,那么B={3,-2,2,-3}
所以,A∪B={2,3,4,-2,-3}