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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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