若A={x|x^2-4x+3=0},B={x|x^2-ax+a-1=0},C={x|x^2-mx+1=0}且A∪B=A,A∩C=C,求实数a、m的值或取值范围.
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若A={x|x^2-4x+3=0},B={x|x^2-ax+a-1=0},C={x|x^2-mx+1=0}且A∪B=A,A∩C=C,求实数a、m的值或取值范围.
若A={x|x^2-4x+3=0},B={x|x^2-ax+a-1=0},C={x|x^2-mx+1=0}且A∪B=A,A∩C=C,求实数a、m的值或取值范围.
若A={x|x^2-4x+3=0},B={x|x^2-ax+a-1=0},C={x|x^2-mx+1=0}且A∪B=A,A∩C=C,求实数a、m的值或取值范围.
A∪B=A,A∩C=C
即B和C都是A的子集
A的解是x=1,x=3
A={1,3}
B
(x-a+1)(x-1)=0
x=a-1,x=1
B是A的子集
则a-1=1或a-1=3
a=2,a=4
C
若C是空集
则判别式小于0
m²-4
A={x|x^2-4x+3=0}
={x| (x-1)(x-3)=0}
={1,3}
B={x|x^2-ax+a-1=0}
={x| (x-1)(x-(a-1))=0}
= { 1, a-1}
A∪B=A => B is subset of A
a-1 = 1 => a=2 or
a-1 =3 => a=4
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A={x|x^2-4x+3=0}
={x| (x-1)(x-3)=0}
={1,3}
B={x|x^2-ax+a-1=0}
={x| (x-1)(x-(a-1))=0}
= { 1, a-1}
A∪B=A => B is subset of A
a-1 = 1 => a=2 or
a-1 =3 => a=4
a= 2 or 4 #
A∩C=C => C is subset of A
C={x|x^2-mx+1=0}
when x= 1
1-m+1 =0
m =2
when x= 3
9-m+1 =0
m =10
m =2 or 10 #
收起
依题意得：A={1,3}，B、C包含于A，
所以：a=2，m=2