Three positive real numbers
Source: Indonesia Mathematics Olympiad 2007 Day 1 Problem 3
June 2, 2008
inequalitiesinequalities proposed
Problem Statement
Let be positive real numbers which satisfy 5(a^2\plus{}b^2\plus{}c^2)<6(ab\plus{}bc\plus{}ca). Prove that these three inequalities hold: a\plus{}b>c, b\plus{}c>a, c\plus{}a>b.