Question:
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 $\frac{a_{10}-2 a_{8}}{3 a_{9}}$ is:
Correct Option: 1
Solution:
$\alpha^{2}-6 \alpha-2=0$
$\alpha^{10}-6 \alpha^{9}-2 \alpha^{8}=0$
$\Rightarrow a_{10}-6 a_{9}-2 a_{8}=0$
$\Rightarrow \frac{\mathrm{a}_{10}-2 \mathrm{a}_{8}}{3 \mathrm{a}_{9}}=2$
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