Question 68
Find all functions $f : \mathbb{R} \to \mathbb{R}$ satisfying the following conditions:
(i) there is at most one number $a$ such that $f(a) = 0,$
(ii) $f(f(x+y)f(x-y) + 25xy + y^2) = 24yf(x) + xf(x+y)$ for all real $x, y$.
(i) there is at most one number $a$ such that $f(a) = 0,$
(ii) $f(f(x+y)f(x-y) + 25xy + y^2) = 24yf(x) + xf(x+y)$ for all real $x, y$.