Not that Tedious

Algebra Level 5

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

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

ω=1xy+z1+1yz+x1+1zx+y1\large{\omega = \dfrac{1}{xy+z-1} + \dfrac{1}{yz+x-1} + \dfrac{1}{zx+y-1} }

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

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