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3

Part of 2007 Indonesia MO

Problems(1)

Three positive real numbers

Source: Indonesia Mathematics Olympiad 2007 Day 1 Problem 3

6/2/2008
Let a,b,c a,b,c 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.
inequalitiesinequalities proposed