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Best constant

Source: Greek national M.O. 2004, Final Round,problem 1

November 15, 2011
inequalitiesrearrangement inequalityinequalities unsolved

Problem Statement

Find the greatest value of MM ∈R\in \mathbb{R} such that the following inequality is true ∀\forall x,y,zx, y, z ∈R\in \mathbb{R} x4+y4+z4+xyz(x+y+z)≥M(xy+yz+zx)2x^4+y^4+z^4+xyz(x+y+z)\geq M(xy+yz+zx)^2.
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