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

Source: 1998 Estonia National Olympiad Final Round grade 10 p1

March 14, 2020
inequalitiesalgebra

Problem Statement

Prove that for any reals a>b>ca> b> c, the inequality a2(b−c)+b2(c−a)+c2(a−b)>0a^2(b - c) + b^2(c - a) + c^2(a - b)> 0.
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