# A number theory problem by Dragan Marković

$\large{\begin{cases} x^2+y^2+z^2=18 \\ xy+yz+zx = 9 \end{cases}}$

Let $$x,y$$ and $$z$$ be integers satisfying the system of equations above. Find $$|x| + |y| + |z|$$.

Notation: $$| \cdot |$$ denotes the absolute value function.

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