JEE-Mains 2015 (3/30)

Algebra Level 3

Let \(\alpha\) and \(\beta\) be the roots of equation \(x^2-6x-2=0\).

If \(a_n=\alpha^n-\beta^n\) for \(n \geq 1,\) then the value of \(\dfrac{a_{10}-2a_8}{2a_9}\) is equal to \(\text{__________}.\)