Algebra Level 2

If $$a$$ and $$b$$ are the roots of the equation $$x^2 - 6x - 2 = 0$$ and $$k_n = a^n - b^n$$, where $$n \in \mathbb N$$, find $$\dfrac{k_{10} - 2 k_{8}}{2 k_{9}}$$.

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