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Symmetric 3-variable inequality

Source: Turkey JBMO Team Selection Test Problem 4

May 29, 2012
inequalitiesfunctioninequalities proposed3-variable inequality

Problem Statement

Find the greatest real number MM for which a2+b2+c2+3abc≥M(ab+bc+ca) a^2+b^2+c^2+3abc \geq M(ab+bc+ca) for all non-negative real numbers a,b,ca,b,c satisfying a+b+c=4.a+b+c=4.
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