Let α and β be the roots of x2−6x−2=0, with α>β. If an=αn−βn for n≥1, then the value of a10−2a82a9 is

an=αn−βnAlso α2−6α−2=0Multiply with α8 on both sides⇒ α10−6α9−2α8=0                …… (1)similarly β10−6β9−2β8=0           ……. (2)Subtracting (2) from (1) we haveα10−β10−6α9−β9=2α8−β8⇒a10−6a9=2a8⇒a10−2a82a9=3.