已知集合A={-1,a2+1,a2-3},B={-4,a-1,a+1},且A∩B={-2},求A∪B.
已知集合A={-1,a2+1,a2-3},B={-4,a-1,a+1},且A∩B={-2},求A∪B.
解因为A∩B={-2},所以-2∈A,且-2∈B.
又因为-1≠-2,a2+1≥1≠-2,
所以a2-3=-2,解得a=±1.
当a=1时,A={-1,2,-2},B={-4,0,2},则A∩B={2},不符合题意;
当a=-1时,A={-1,2,-2},B={-4,-2,0},则A∩B={-2},符合题意.
故A∪B={-1,2,-2,-4,0}.