Question

若a,x属于R,集合A={2,4,x^2减5x+9},B={3,x^2+ax+a},C={x^2+(a+1)x减3,1}求(1)使A={2,3,4}的x的值 (2)使...

若a,x属于R,集合A={2,4,x^2减5x+9},B={3,x^2+ax+a},C={x^2+(a+1)x减3,1}求(1)使A={2,3,4}的x的值 (2)使B=C的a,x的值 急

Answer 1

1. x=2,x=3 2. x=-1 a=-6 或者 x=3 a=-2

Answer 2

(1)x^2-5x+9=3
x^2-5x+6=0
(x-2)(x-3)=0
x=2或3
(2)x^2+ax+a=1
x^2+(a+1)x-3=3
两式相减
x-3-a=2
x=5+a
(5+a)^2+a(5+a)+a=1
25+a^2+10a+5a+a^2+a-1=0
a^2+8a+12=0
a=-2或a=-6
x=3或x=-1