Complex solutions

Algebra Level 4

\(x, y\) and \(z\) are complex numbers such that

\[ \begin{cases} x + y + z & = 20 \\ (x-y)^2 + (y-z)^2 + (z-x) ^ 2 & = xyz.\\ \end{cases} \]

What is the value of \( \frac{ x^3 + y^3 + z^3} { xyz} \)?

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