Mathematics - Quadratic Equation Question with Solution | TestHub

${\alpha }^2-6\alpha -2=0$

$\begin{array}{c}{\alpha }^{10}-6{\alpha }^9-2{\alpha }^8=0\\ \underline{{\beta }^{10}-6{\beta }^9-2{\beta }^8=0}\\ \left({\alpha }^{10}-{\beta }^{10}\right)-6\left({\alpha }^9-{\beta }^9\right)-2\left({\alpha }^8-{\beta }^8\right)=0\end{array}$

$\Rightarrow a_{10}-6a_9-2a_8=0$

$\Rightarrow \frac{a_{10}-2a_8}{3a_9}=2$