Question

已知A={x|x²+px+q=x}B=P{x|(x-1)²+p（x-1)+q=x+1}当A={2}时，求集合B

请尽量快点解出来~~

Answer 1

x²+px+q=x方程根就是x=2
代入q=-2-2p
△=p^2-2p+1-4q=p^2-2p+1+8+8p=0
p^2+6p+9=0
p=-3
q=4
(x-1)²+p（x-1)+q=x+1
x^2-2x+1-3x+3+4-x-1=0
x^2-6x+7=0
△=36-28=8
B={3±根号2}

Answer 2

∵A={2} ∴2p+q=-2且(p-1)^2-4q=0解得p=-3且q=4把p，q代入B求解即可