Real constants
are such that there is exactly one square all of whose vertices lie on the cubic curve
Prove that the square has sides of length
![\sqrt[4]{72}.](/media/m/5/4/c/54c66832c053970e63876cd79459f032.png)
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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 $\sqrt[4]{72}.$
Školjka