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Regional Olympiad - FBH 2015 Grade 12 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2015

September 23, 2018
inequalitiesalgebra

Problem Statement

Let aa, bb, cc and dd be real numbers such that a+b+c+d=8a+b+c+d=8. Prove the inequality: a8+b−d3+b8+c−a3+c8+d−b3+d8+a−c3≥4\frac{a}{\sqrt[3]{8+b-d}}+\frac{b}{\sqrt[3]{8+c-a}}+\frac{c}{\sqrt[3]{8+d-b}}+\frac{d}{\sqrt[3]{8+a-c}} \geq 4
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