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(a^{-3}+b)/(1-a)+(b^{-3}+c)/(1-b)+(c^{-3}+a)/(1-c)>= 123 if a+b+c=1, a,b,c>0

Source: IMAC Arhimede 2012 p6

May 6, 2019
algebrainequalitiesthree variable inequality

Problem Statement

Let a,b,ca,b,c be positive real numbers that satisfy the condition a+b+c=1a + b + c = 1. Prove the inequality a−3+b1−a+b−3+c1−b+c−3+a1−c≥123\frac{a^{-3}+b}{1-a}+\frac{b^{-3}+c}{1-b}+\frac{c^{-3}+a}{1-c}\ge 123
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