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Function related to (x+y)^2

Source: European Girls’ Mathematical Olympiad-2014 - Day 2 - P6

April 13, 2014
functionquadraticsalgebrafunctional equationEGMOEGMO 2014

Problem Statement

Determine all functions f:R→Rf:\mathbb R\rightarrow\mathbb R satisfying the condition f(y2+2xf(y)+f(x)2)=(y+f(x))(x+f(y))f(y^2+2xf(y)+f(x)^2)=(y+f(x))(x+f(y)) for all real numbers xx and yy.
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