Let α and β be the roots of equation x² - 6x - 6 = 0. If an = αn - βn, for n ≥ 1, then the value of a10 - 6a8 / 2a9 is equal to

Let α, β be the roots ⇒ α² - 6α - 6 = 0 ⇒ α² - 6 = 6α and β² - 6β - 6 = 0 ⇒ β² - 6 = 6β
Hence, a10 - 6a8 / 2a9 = α10 - β10 - 6(α8 - β8) / 2(α9 - β9) = α8(α² - 6) - β8(β² - 6) / 2(α9 - β9) = α8(6α) - β8(6β) / 2(α9 - β9) = 6(α9 - β9) / 2(α9 - β9) = 3