An algebra problem by vansh gupta

Algebra Level 3

Let \(a\) and \(b\), where \(a>b\), be the roots of the equation \(x^2 - 6x - 2= 0 \). Denote \(\alpha_n = a^n + b^n\), where \(n\) is a positive integer. Find the value of \( \dfrac{\alpha_{10} - 2\alpha_8}{2\alpha_9} \).

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