Three equations, three variables, three powers

Algebra Level 4

\[\begin{cases} x + y + z = 10 \\ x^2 + y^2 + z^2 = 20 \\ x^3 + y^3 + z^3 = 100 \end{cases}\]

Consider three complex numbers \( x, y\) and \( z \) that satisfy the system of equations above. Find the value of \( xyz \).

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