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Best constant

Source: Greek national M.O. 2000, Final Round, problem 3

November 20, 2011
inequalities unsolvedinequalities

Problem Statement

Find the maximum value of kk such that xy(x2+y2)(3x2+y2)≤1k\frac{xy}{\sqrt{(x^2 + y^2)(3x^2 + y^2)}}\leq \frac{1}{k} holds for all positive numbers xx and y.y.
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