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Four-Variables Inequality - Switzerland 2011

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March 22, 2011
inequalitiesinequalities proposed

Problem Statement

Let a,b,c,da, b, c, d be positive real numbers satisfying a+b+c+d=1a+b+c+d =1. Show that \frac{2}{(a+b)(c+d)} \leq \frac{1}{\sqrt{ab}}+ \frac{1}{\sqrt{cd}}\mbox{.}
(Swiss Mathematical Olympiad 2011, Final round, problem 6)
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