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Find the dimensions of the rectangular solid of largest volume which can be inscribed in the...

Find the dimensions of the rectangular solid of largest volume which can be inscribed in the ellipsoid

x2/16+y2/4+z2/9=1

Hint: Let (?, ?, ?) represent one of the eight vertices of the solid. Then by symmetry the volume of the solid is ? = (2?)(2?)(2?).

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