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 :

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

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.