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(a^3 - c^3)/3 \ge abc [(a- b)/c+ (b- c)/a]

Source: Nordic Mathematical Contest 1988 #2

October 5, 2017
inequalities

Problem Statement

Let a,b,a, b, and cc be non-zero real numbers and let a≥b≥ca \ge b \ge c. Prove the inequality a3−c33≥abc(a−bc+b−ca)\frac{a^3 - c^3}{3} \ge abc (\frac{a- b}{c}+ \frac{b- c}{a}) . When does equality hold?
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