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[(a^2-b^2)^3 + (b^2- c^2)^3 + (c^2 - a2)^3][(a-b)^3 + (b-c)^3 + (c-a)^3]> 8sbc

Source: New Zealand NZMOC Camp Selection Problems 2011 Seniors 5

September 18, 2021
algebrainequalities

Problem Statement

Prove that for any three distinct positive real numbers a,ba, b and cc: (a2−b2)3+(b2−c2)3+(c2−a2)3(a−b)3+(b−c)3+(c−a)3>8abc.\frac{(a^2 - b^2)^3 + (b^2 - c^2)^3 + (c^2 - a^2)^3}{(a - b)^3 + (b - c)^3 + (c - a)^3}> 8abc.
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