Question

设集合A={1,a,a2}B={1,a,b}且A并B等于{1,3}A交B等于{1...

设集合A={1,a,a2}B={1,a,b}且A并B等于{1,3}A交B等于{1,a,2a,3a}求ab

Answer 1

A∩B={1,3},A∪B={1,a,2a,3a}a=3时,A={1,3,9},B={1,3,b},A∪B={1,3,6,9},所以b=6.a²=3时,a=√3或-√3.A={1,3,√3}或{1,3,-√3}
A∪B={1,√3,2√3,3√3}或
A∪B={1,-√3,-2√3,-3√3}不符合题意综上a=3,b=6.