Let $\alpha $ and $\beta $ be the roots of equation ${x^2} - 6x - 2 = 0$. If ${a_n} = {\alpha ^n} - {\beta ^n},$ for $n \ge 1,$ then the value of ${{{a_{10}} - 2{a_8}} \over {2{a_9}}}$ is equal to :
$3$
$ - 3$
$6$
$ - 6$
Solution
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