# Find a general solution for the lengths of the sides of the rectangular parallelepiped with the

largest volume that can be inscribed in the following ellipsoid

largest volume that can be inscribed in the ellipsoid defined by $x^2/a^2 + y^2/b^2 + z^2/c^2 = 1$, where a, b, and c are positive real constants. Definitions: A parallelepiped is a three dimensional object with 6 sides, all of which are parallelograms; inscribed means that the boundaries touch but do not cross.

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