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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