Using Vieta's Formula?

Algebra Level 4

2016x3+2015x2+2014x+2016=0\large 2016x^{3}+2015x^{2}+2014x+2016=0

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

Find the value of :

2016(α3+β3+γ3)+2015(α2+β2+γ2)+2014(α+β+γ)2016(α3β3γ3)+2015(α2β2γ2)+2014(αβγ)\dfrac{2016(\alpha^3+\beta^3+\gamma^3)+2015(\alpha^2+\beta^2+\gamma^2)+2014(\alpha+\beta+\gamma)}{2016(\alpha^3-\beta^3-\gamma^3)+2015(\alpha^2-\beta^2-\gamma^2)+2014(\alpha-\beta-\gamma)}

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