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sum a^2 (a - b)(a + b) >0

Source: Switzerland - 2013 Swiss MO Final Round p8

January 14, 2023
algebrainequalities

Problem Statement

Let a,b,c>0a, b, c > 0 be real numbers. Show the following inequality: a2⋅a−ba+b+b2⋅b−cb+c+c2⋅c−ac+a≥0.a^2 \cdot \frac{a - b}{a + b}+ b^2\cdot \frac{b - c}{b + c}+ c^2\cdot \frac{c - a}{c + a} \ge 0 . When does equality holds?
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