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Largest real constant lambda(a,b,c>0)

Source: Regional Mathematical Olympiad 2, India

December 31, 2011
inequalitiesinequalities proposedindia2011

Problem Statement

Find the largest real constant λ\lambda such that λabca+b+c≤(a+b)2+(a+b+4c)2\frac{\lambda abc}{a+b+c}\leq (a+b)^2+(a+b+4c)^2 For all positive real numbers a,b,c.a,b,c.
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