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\Sum_{cyclic}\frac{a-\sqrt[3]{bcd}}{a+3(b+c+d)}\ge 0 for a,b,c,d>0

Source: IMAC Arhimede 2014 p6

May 6, 2019
algebrainequalitiescyclic inequalityfour variables

Problem Statement

If a,b,c,da, b, c, d are positive numbers, prove that ∑cyclica−bcd3a+3(b+c+d)≥0\sum_{cyclic}\frac{a-\sqrt[3]{bcd}}{a+3(b+c+d)}\ge 0
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