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Inequality in 6 Variables.

Source: European Mathematical Cup 2012, Senior Division, Problem 3

July 27, 2013

inequalitiesinequalities proposed

Problem Statement

Prove that the following inequality holds for all positive real numbers

a

b

c

d

e

and

f

\sqrt[3]{\frac{abc}{a+b+d}}+\sqrt[3]{\frac{def}{c+e+f}} < \sqrt[3]{(a+b+d)(c+e+f)} \text{.}

Proposed by Dimitar Trenevski.