已知集合A=｛x|x^2-3x+2=0},B={x|x^2-ax+a-1=0},C=｛x|x-x+2m=0}.若AUB=A,A∩C=C,求a,m的取值范围.

题目

已知集合A=｛x|x^2-3x+2=0},B={x|x^2-ax+a-1=0},C=｛x|x-x+2m=0}.若AUB=A,A∩C=C,求a,m的取值范围.
我希望有完整的解题过程.

答案

A=｛x|x^2-3x+2=0}
= {x|(x-1)(x-2)=0
= {1,2}
AUB=A => B is subset of A
when x=1,B={x|x^2-ax+a-1=0},
1-a+a-1=0 => 0=0
when x=2
4-2a+a-1=0
a=3 #
A∩C=C => C is subset of A
when x=1,C=｛x|x^2-x+2m=0}
1-1+2m =0
m =0
when x=2
4-2+2m =0
m = -1
m = 0 or -1#