已知a,x∈R,集合A={2,4,x²-5x+9},B={3,x²+ax+a}A={2,3,4,}若2∈B,B是A的真子集,求a,x的值

Question

已知a,x∈R,集合A={2,4,x²-5x+9},B={3,x²+ax+a} A={2,3,4,} 若2∈B,B是A的真子集,求a,x的值

Answer 1

2∈B,then
x²+ax+a = 2
x²+ax+(a-2) =0 --（1）
B是A的真子集
x²-5x+9 = 3
x²-5x+6 =0
(x-2)(x-3)=0
x = 2 or 3 #
when x=2
from (1)
4+2a+(a-2) =0
a = -2/3 #
when x=3
9+3a+(a-2)=0
a= -7/4 #