Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
Let α and β be the roots of equation x2-6x-2=0. If an=αn-βn,  n1, then the value of a10-2a82a9 is equal to
MathematicsQuadratic EquationJEE MainJEE Main 2015 (04 Apr)
Options:
  • A -3
  • B 6
  • C -6
  • D 3
Solution:
1218 Upvotes Verified Answer
The correct answer is: 3

Given, α, β are roots of x2-6x-2=0.

⇒ α2-6α-2=0 and  β2-6β-2=0

⇒  α2-2=6α andβ2-2=6β  ...1

a10-2a82a9=α10-β10-2α8-β82α9-β9

=α10-2α8-β10-2β82α9-β9

= α 8 α 2 - 2 - β 8 β 2 - 2 2 α 9 - β 9

= α 8 6 α - β 8 6 β 2 α 9 - β 9        [  From (1)]

 =6α9-6β92α9-β9=3

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.