Using Vieta's Formula? (2)

Algebra Level 5

$\large 2017x^3+2016x^2+2015x+2016=0$

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

Find the value of :

$\large \dfrac{2017(\alpha^3-\beta^3-\gamma^3)+2016(\alpha^2-\beta^2-\gamma^2)+2015(\alpha-\beta-\gamma)}{\sqrt[4]{\alpha^4\beta^3\gamma^3+\alpha^3\beta^4\gamma^3+\alpha^3\beta^3\gamma^4}}$