Turkey NMO 2008 Problem 3
Source: Turkey NMO 2008 Problem 3
December 1, 2008
inequalitiesLaTeXinequalities unsolved
Problem Statement
Let a.b.c be positive reals such that their sum is 1. Prove that
\frac{a^{2}b^{2}}{c^{3}(a^{2}\minus{}ab\plus{}b^{2})}\plus{}\frac{b^{2}c^{2}}{a^{3}(b^{2}\minus{}bc\plus{}c^{2})}\plus{}\frac{a^{2}c^{2}}{b^{3}(a^{2}\minus{}ac\plus{}c^{2})}\geq \frac{3}{ab\plus{}bc\plus{}ac}