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Vertices lie on the cubic curve y = x^3 + ax^2 + bx + c

Source: IMO ShortList 1991, Problem 22 (USA 4)

August 15, 2008
algebrasquareCubicpolynomialcubic equationIMO Shortlist

Problem Statement

Real constants a,b,c a, b, c are such that there is exactly one square all of whose vertices lie on the cubic curve y \equal{} x^3 \plus{} ax^2 \plus{} bx \plus{} c. Prove that the square has sides of length 724. \sqrt[4]{72}.
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