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

Source: Oliforum Contest III 2012 p4 https://artofproblemsolving.com/community/c2487525_oliforum_contest

September 28, 2021
algebrainequalities

Problem Statement

Show that if a≥b≥c≥0a \ge b \ge c \ge 0 then a2b(a−b)+b2c(b−c)+c2a(c−a)≥0.a^2b(a - b) + b^2c(b - c) + c^2a(c - a) \ge 0.
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