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sum (a-b)(b+c) >=0

Source: Switzerland - 2009 Swiss MO Final Round p3

December 26, 2022
algebrainequalities

Problem Statement

Let a,b,c,da, b, c, d be positive real numbers. Prove the following inequality and determine all cases in which the equality holds : a−bb+c+b−cc+d+c−dd+a+d−aa+b≥0.\frac{a - b}{b + c}+\frac{b - c}{c + d}+\frac{c - d}{d + a}+\frac{d - a}{a + b} \ge 0.
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