Let \( \alpha \) and \( \beta \) be the roots of \( x^{2}-6 x-2=0 \). If \( a_{n}=\alpha^{n}-\beta^{n} \) for \( n \geq …

Let \( \alpha \) and \( \beta \) be the roots of \( x^{2}-6 x-2=0 \). If \( a_{n}=\alpha^{n}-\beta^{n} \) for \( n \geq 1 \), then the value of \( \frac{a_{10}-2 a_{8}}{3 a_{9}} \)

[JEE Main 2021, 25 Feb (Shift 2)]