# 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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