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Let α\alphaα and β\betaβ be the roots of x2−6x−2x^{2} - 6x -2x2−6x−2 , with α>β\alpha > \betaα>β. If an=αn−βna_{n} = \alpha^{n} - \beta^{n}an=αn−βn for n>1n>1n>1, then find the value of a10−2a82a9\dfrac{a_{10} - 2a_{8}}{2a_{9}}2a9a10−2a8.
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