Let `alpha` and `beta` be the roots of equation `x^2-6x-2""=""0` . If `a_n=alpha^n-beta^n ,""for""ngeq1` , then the value of `(a_(10)-2a_8)/(2a_9)` is equal to: (1) 6 (2)`-6` (3) 3 (4) `-3`

Explanation

To solve the problem, we need to find the value of \((a_{10} - 2a_8) / (2a_9)\) given that \(\alpha\) and \(\beta\) are the roots of the equation \(x^2 - 6x - 2 = 0\) and \(a_n = \alpha^n - \beta^n\) for \(n \geq 1\).

### Step 1: Find the roots \(\alpha\) and \(\beta\)
We start by solving the quadratic equation \(x^2 - 6x - 2 = 0\) using the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
...