Question

已知集合A={x|x2-3x+2=0},B={x|x2-ax+a-1=0},C={x|x2-mx+1=0},且A∪B=A

Answer 1

A={x|x^2-3x+2=0}

= {1,2}

B={x|x^2-ax+a-1=0}

= { 1,(a-1)}

C={x|x2-mx+1=0}

A∪B=A

=> B is subset of A

when x=1

a-1=1 => a=2

when x=2

a-1=2 => a=3

ie a= 2 or 3

A∩C=C

=> C is subset of A

when x=1

1-m+1=0 => m=2

when x=2

4-2m+1=0 => m=5/2

ie m=2 or 5/2