Tetracube

Geometry Level 5

The side length of the largest cube that can fit inside a regular tetrahedron whose edges have an unit length of one, can be represented by the formula

\[ \dfrac{ \sqrt{AB} }{A + \sqrt{AB} + B\sqrt B} , \]

where \(A\) and \(B\) are coprime positive integers. Find \(A+B\).

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