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system x^2 + x = y^3 - y, y^2 + y = x^3 - x

Source: 2014 Austrian Federal Competition For Advanced Students, Part 1 p1

February 2, 2020
system of equationsalgebra

Problem Statement

Determine all real numbers xx and yy such that x2+x=y3−yx^2 + x = y^3 - y, y2+y=x3−xy^2 + y = x^3 - x
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