1) Let α and β be the roots of x2−6x−2=0 with α>β , if an=αn−βn for ≥1, then the value of a10−2a82a9 is A) 1 B) 2 C) 3 D) 4 Answer: Option CExplanation:a10−2a82a9=(α10−β10)−2(α8−β8)2(α9−β9) =α8(α2−2)−β8(β2−2)2(α9−β9) [ ∴ is root of x2−6x−2=0 α2−2=6α] Also,β is the root of x2−6x−2=0 → β2−2=6β =α8(6α)−β8(6β)2(α9−β9)=6(α9−β9)2(α9−β9)=3