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Let $\alpha$ and $\beta$ be the roots of equation $x^2-6x-2=0$.

If $a_n=\alpha^n-\beta^n$ for $n \geq 1,$ then the value of $\dfrac{a_{10}-2a_8}{2a_9}$ is equal to $\text{\_\_\_\_\_\_\_\_\_\_}.$

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