# Problem maximized!

Algebra Level 4

$$x,y$$ and $$z$$ are positive reals satisfying $$x+y+z = 10$$.

If the maximum value of $$xyz + xy + yz + zx$$ can be expressed as $$\dfrac AB$$, where $$A$$ and $$B$$ are coprime positive integers, find $$A+B$$.

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