Not that Tedious

Algebra Level 5

\[\large{ \begin{cases} x+y+z=2 \\ xy+yz+zx=0.5 \\ xyz=4 \end{cases} }\]

Let \(x,y,z\) be complex numbers that satisfies the above system of equations. Define \(\omega\) as:

\[\large{\omega = \dfrac{1}{xy+z-1} + \dfrac{1}{yz+x-1} + \dfrac{1}{zx+y-1} }\]

Evaluate the value of \( \large{-18\omega}\) correct up to one place of decimal.

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