Real constants
![a, b, c](/media/m/9/e/9/9e9dfe78930065fbe5a777e9b07c27c4.png)
are such that there is exactly one square all of whose vertices lie on the cubic curve
![y = x^3 + ax^2 + bx + c.](/media/m/2/f/e/2febff95c27baaef18b2266021df3cd6.png)
Prove that the square has sides of length
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Real constants $a, b, c$ are such that there is exactly one square all of whose vertices lie on the cubic curve $y = x^3 + ax^2 + bx + c.$ Prove that the square has sides of length $\sqrt[4]{72}.$