# An algebra problem by vansh gupta

Algebra Level 3

Let $$a$$ and $$b$$, where $$a>b$$, be the roots of the equation $$x^2 - 6x - 2= 0$$. Denote $$\alpha_n = a^n + b^n$$, where $$n$$ is a positive integer. Find the value of $$\dfrac{\alpha_{10} - 2\alpha_8}{2\alpha_9}$$.

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