Question

高一数学集合题，求过程快！

已知a，x∈R，集合A={2,4，x^2-5x+9}，B={3，x^2+ax+a}，C={x^2+（a+1）x-3,1},求;
使2∈B,B是A的真子集的a,x的值。

Answer 1

2∈B
=> x^2+ax+a =2
B is subset of A
=> x^2-5x+9 =3
for
x^2-5x+9 =3
(x-2)(x-3)=0
x = 2 or 3 #

for x=2, x^2+ax+a =2
4+2a+a =2
a = -2/3 #
for x=3
9+3a+a =2
a = -7/4 #

or

x^2+ax+a = x^2-5x+9