# What's the fastest approach?

Algebra Level 4

Let $\alpha$ and $\beta$ be the roots of $x^2 - 6x - 2 = 0$, with $\alpha > \beta$. If $a_n = \alpha ^n - \beta ^n$ for $n\ge 1$, then find the value of:

$\frac {a_{10} - 2a_8} {2a_9}$

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