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the minimum value of [(a^3+b^3+c^3)/abc]^2

Source: Austrian Mathematical Olympiad 2003, Part 2, D1, P2

June 18, 2011
geometrygeometric transformationrotationinequalities unsolvedinequalities

Problem Statement

Let a,b,ca, b, c be nonzero real numbers for which there exist α,β,γ∈{−1,1}\alpha, \beta, \gamma \in\{-1, 1\} with \alpha a + \beta b + \gamma c = 0. What is the smallest possible value of (a3+b3+c3abc)2?\left( \frac{a^3+b^3+c^3}{abc}\right)^2 ?
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