IMO 2023 Shortlist A2
Let R be the set of real numbers. Let f : R Ñ R be a function such that fpx yqfpx ´ yq ě fpxq2 ´ fpyq2 for every x,y P R...
Category: Algebra
Problem
Let R be the set of real numbers. Let f : R Ñ R be a function such that fpx ` yqfpx ´ yq ě fpxq2 ´ fpyq2 for every x,y P R. Assume that the inequality is strict for some x0,y0 P R. Prove that fpxq ě 0 for every x P R or fpxq ď 0 for every x P R. (Malaysia)