Using Vieta's Formula? (3)

Algebra Level 4

\[\large 2017x^3+2016x^2+2018x+2016=0\]

Let \(\alpha\) , \(\beta\) and \(\gamma\) be the roots of the equation above.

Find the value of :

\[\large \dfrac{2017(\alpha^3-\beta^3-\gamma^3)+2016(\alpha^2-\beta^2-\gamma^2)+2018(\alpha-\beta-\gamma)}{\sqrt[8]{2(\alpha^{6}\beta^{7}\gamma^{7}+\alpha^{7}\beta^{6}\gamma^{7}+\alpha^{7}\beta^{7}\gamma^{6})+(\alpha^{8}\beta^{6}\gamma^{6}+\alpha^{6}\beta^{8}\gamma^{6}+\alpha^{6}\beta^{6}\gamma^{8})} }\]

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