全集I={1.2a-4.a^2-a-3},A={a-1,1}.A的补集为{3}.那a的值是( ).

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全集I={1.2a-4.a^2-a-3},A={a-1,1}.A的补集为{3}.那a的值是( ).
全集I={1.2a-4.a^2-a-3},A={a-1,1}.A的补集为{3}.那a的值是( ).

全集I={1.2a-4.a^2-a-3},A={a-1,1}.A的补集为{3}.那a的值是( ).
I = {1,2a-4, a^2-a-3 }
A = {a-1, 1}
case 1
a-1 = 2a-4 and a^2-a-3 =3
=>a=3 and (a-3)(a+2) =0
=>a=3 and a=3 or -2
=> a=3
case 2
2a-4 = 3 and a^2-a-3 = a-1
=> a = 7/2 and a^2-2a-2 =0
=> a = 7/2 and a = 1+√3 or 1-√3
=> no solution
case 1 or case 2
ie a=3

a=3
∵A的补集为{3}
∴I-A={3}
假设
(1)若2a-4=a-1,那么a=3
将a=3带入,则I={1.2.3},A={2,1}符合题意
(2)若a^2-a-3=a-1,那么该方程无解
综上可知,a=3