Problem

Source: Bulgarian National Olympiad 2006 First day problem 2

Tags: function, limit, induction, inequalities, algebra proposed, algebra



Let $f:\mathbb{R}^+\to\mathbb{R}^+$ be a function that satisfies for all $x>y>0$ \[f(x+y)-f(x-y)=4\sqrt{f(x)f(y)}\] a) Prove that $f(2x)=4f(x)$ for all $x>0$; b) Find all such functions. Nikolai Nikolov, Oleg Mushkarov