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\frac{a}{c+5b}+\frac{b}{a+5c}+\frac{c}{b+5a}\geq\frac{1}{2} , for a,b,c>0

Source: KJMO 2007 p5

May 2, 2019
algebrainequalitiesInequalitythree variable inequality

Problem Statement

For all positive real numbers a,b,c.a, b,c. Prove the folllowing inequalityac+5b+ba+5c+cb+5a≥12.\frac{a}{c+5b}+\frac{b}{a+5c}+\frac{c}{b+5a}\geq\frac{1}{2}.
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