Question 51

Let $$\alpha$$ and $$\beta$$ be the roots of $$x^2 - 6x - 2 = 0$$, with $$\alpha > \beta$$. If $$a_n = \alpha^n - \beta^n$$ for $$n \geq 1$$, then the value of $$\frac{a_{10} - 2a_8}{2a_9}$$ is

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