Let  α and β be the roots of equation X2 - 6x - 2 = O. If an=αn−βn, for n≥1,then the value a10−2a82a9 as is equal to

Given,α and β are the roots of the equationx2−6x−2=0∵an=αn−βn for n≥1∴ a10=α10−β10 a8=α8−β8⇒a9=α9−β9Now, considera10−2a82a9=α10−β10−2α8−β82α9−β9=α8α2−2−β8β2−22α9−β9=α8⋅6α−β8⋅6β2α9−β9=6α9−6β92α9−β9=62=3∣∵α and β are the  roots of x2−6x−2=0 or  x2=6x+2⇒ α2=6α+2⇒α2−2=6α and β2=6β+2⇒β2−2=6β