Question

已知x∈R，集合A={-3，x2 ，x+1}，B={x-3，2x-1，x2 +1},如果A∩B={-3}，求A∪B。要详细过程

Answer 1

A∩B={-3}, B={x-3，2x-1，x2 +1},x2 +1>0
若x-3=-3，即x=0，则A={-3,0,1},B={-3,-1,1}
此时A∩B={-3,1}不符合题意，舍去
那么2x-1=-3，即x=-1，A={-3,0,1},B={-4,-3,2}
A∪B={-3,0,1-4,2}

Answer 2

if A∩B={-3}
=> x-3 =-3 or 2x-1=-3 or x2 +1=-3
=> x=0 or x=-1

when x=0
A= {-3, 0, 1} , B ={-3,-1, 1} (rejected)
∵A∩B ={ -3,1}

when x=-1
A= {-3,1,0}, B={-4, -3, 2}
=> A∩B ={-4,-3,0,1,2} #