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only 1 square with vertices on graph of y = x^3 + ax

Source: 1993 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p2

November 20, 2022
analytic geometrysquaregeometry

Problem Statement

For the real number aa it holds that there is exactly one square whose vertices are all on the graph with the equation y=x3+axy = x^3 + ax. Find the side length of this square.
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