Using Vieta's Formula? (2)

Algebra Level 5

2017x3+2016x2+2015x+2016=0\large 2017x^3+2016x^2+2015x+2016=0

Let α\alpha , β\beta and γ\gamma be the roots of the equation above .

Find the value of :

2017(α3β3γ3)+2016(α2β2γ2)+2015(αβγ)α4β3γ3+α3β4γ3+α3β3γ44\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}}

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