# Are vieta's formulas required

Algebra Level 4

Let $$A$$ and $$B$$ be the roots of the polynomial $$x^2-17x-2$$. And let $$a_n = A^n - B^n$$. Find $$k= \left \lfloor \dfrac{a_{10} - 2a_8}{2a_9} \right \rfloor$$.

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