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Turkey NMO 2007 Problem 3, inequality with a+b+c=3

Source: Turkey NMO 2007 Problem 3

September 27, 2011
inequalitiesinequalities proposed

Problem Statement

If a,b,ca,b,c are three positive real numbers such that a+b+c=3a+b+c=3, prove that a2+3b2ab2(4−ab)+b2+3c2bc2(4−ab)+c2+3a2ca2(4−ca)≥4 {\frac{a^{2}+3b^{2}}{ab^{2}(4-ab)}}+{\frac{b^{2}+3c^{2}}{bc^{2}(4-ab)}}+{\frac{c^{2}+3a^{2}}{ca^{2}(4-ca)}}\geq 4
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