Problem

Source: 2015 Taiwan TST Round 1 Quiz 1 Problem 2

Tags: function, Taiwan, Function equations, algebra, Taiwan TST 2015



Find all functions $f:\mathbb{Q}\rightarrow\mathbb{R} \setminus \{ 0 \}$ such that \[(f(x))^2f(2y)+(f(y))^2f(2x)=2f(x)f(y)f(x+y)\] for all $x,y\in\mathbb{Q}$