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Indian RMO - Paper -4[3]

Source:

December 12, 2013
cyclic inequality

Problem Statement

Given real numbers a,b,c,d,e>1a,b,c,d,e>1. Prove that a2c−1+b2d−1+c2e−1+d2a−1+e2b−1≥20 \frac{a^2}{c-1}+\frac{b^2}{d-1}+\frac{c^2}{e-1}+\frac{d^2}{a-1}+\frac{e^2}{b-1} \ge 20
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