# IIT JEE Question

Algebra Level 4

Let $$\alpha$$ and $$\beta$$ be the roots of the quadratic equation $$x^2 - 6x - 2$$ with $$\alpha >\beta$$.

Define $$a_n = \alpha^n - \beta^n \quad$$ for integer $$n$$.

Evaluate $\displaystyle \dfrac{ a_{10} }{2 a_9} - \dfrac{ 2 a_8 }{2 a_9 } .$

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