Question

函数f(x)=x2+mx+n,A{x|f(x)=x},B{x|f(x-1)>x+5},若A={3},求集合B? 求解题过程

不要copy的

Answer 1

A={3}
f(x) =x
x^2+mx+n =x
x^2+(m-1)x + n =0

(x-3)^2 =0
x^2-6x+9 =0

m-1 = -6 and n = 9
m = -5 and n = 9
=> f(x) = x^2-5x+9

f(x-1) > x+5
(x-1)^2-5(x-1)+9 > x+5
x^2-8x+10 > 0
x > 4+√6 or x < 4-√6

B = {x | x > 4+√6 or x < 4-√6 }