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 $\text{\_\_\_\_\_\_\_\_\_\_}.$