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Source: Ireland 2002

July 5, 2009
inequalities

Problem Statement

Let 0<a,b,c<1 0<a,b,c<1. Prove the inequality: \frac{a}{1\minus{}a}\plus{}\frac{b}{1\minus{}b}\plus{}\frac{c}{1\minus{}c} \ge \frac {3 \sqrt[3]{abc}}{1\minus{} \sqrt[3]{abc}}. Determine the cases of equality.
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