A number theory problem by Dragan Marković

{x2+y2+z2=18xy+yz+zx=9 \large{\begin{cases} x^2+y^2+z^2=18 \\ xy+yz+zx = 9 \end{cases}}

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

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

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