Question

已知集合A={x|x^2-3x+2=0},B={x|x^2-ax+a-1=0}B包含于A，求a的范围

Answer 1

A:
x²-3x+2=0解得x=1或x=2
B:
△=a²-4(a-1)=(a-2)²≥0，所以B不为空集
x²-ax+a-1=0
得x=1或x=a-1
∵B包含于A
∴a-1=1或a-1=2
得a=2或a=3

Answer 2

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#

Answer 3

a>=3
B包含于A 所以x^2-3x+2>=x^2-ax+a-1
3x-ax+a-3>=0
a-ax>=3-3x
a(1-x)>=3(1-x)
a>=3

Answer 4

a的范围{2, 3}，A={1,2}分析B空集，一解，俩解，又a²-4(a-1)≥0所以不为空集依次分析

Answer 5

a=2或a=3

Answer 6

a=3