# Everyone should love algebra more than geometry

Geometry Level 5

A square having sides parallel to the coordinate axes is inscribed in the region $$\{(x,y): x,y > 0,$$$$y< -x^{3} + 3x\}$$. If the area of the square is written as $$A^{1/3} + B^{1/3}$$ where $$A, B$$ are integers and $$A>B$$, then what is the circum-radius of triangle $$OPQ$$ where $$O$$ is the origin, $$P(A^{1/3},0)$$ and $$Q(0, B^{1/3})$$?

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