# Revival Of This Problem. Part 2

Geometry Level 4

$\begin {cases} a^{2} + ab + b^{2} = 2 \\ b^{2} + bc + c^{2} = 1 \\ c^{2} + ca + a^{2} = 3 \end {cases}$

Let $$a,b,c$$ be all positive numbers satisfying the system of equations above. If $$ab + bc + ca = \cfrac{ x \sqrt{y} } { z}$$, where $$x$$ and $$z$$ are positive coprime integers, and $$y$$ is a squarefree integers, then find $$x + y + z$$.

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