设集合A＝{x^2-4x+3=0},B={x|x^2-ax+a-1=0},C＝{x|x^2-mx+1},若A∪B=A,A∩C=C,求实数a,m的值
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A={x|x^2-4x+3=0}
={x| (x-1)(x-3) =0 }
= {1,3}
A∪B=A
=> B is a subset of A
B={x|x^2-ax+a-1=0}
x=3
x^2-ax+a-1=0
9-3a+a-1=0
a=4
A∩C=C
=> C is a subset of A
C＝{x|x^2-mx+1=0}
x=1
x^2-mx+1=0
1-m+1=0
m=2
x=3
9-3m+1=0
m =10/3
ie m=2 or 10/3
={x| (x-1)(x-3) =0 }
= {1,3}
A∪B=A
=> B is a subset of A
B={x|x^2-ax+a-1=0}
x=3
x^2-ax+a-1=0
9-3a+a-1=0
a=4
A∩C=C
=> C is a subset of A
C＝{x|x^2-mx+1=0}
x=1
x^2-mx+1=0
1-m+1=0
m=2
x=3
9-3m+1=0
m =10/3
ie m=2 or 10/3
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