Quadratic EquationHard
Question
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 
is
is Options
A.1
B.2
C.3
D.4
Solution
an = αn - βn
α2 - 6α - 2 = 0
Multiply with α8 on both sides
⇒ α10 - 6α9 - 2α8 = 08 .......(i)
similarly β10 - 6β9 - 2β8 = 0 .......(ii)
From (i) and (ii)
⇒ α10 - β10 - 6(α9 - β9) = 2 (α8 - β8)
⇒ a10 - 6a9 =2a9 ⇒
α2 - 6α - 2 = 0
Multiply with α8 on both sides
⇒ α10 - 6α9 - 2α8 = 08 .......(i)
similarly β10 - 6β9 - 2β8 = 0 .......(ii)
From (i) and (ii)
⇒ α10 - β10 - 6(α9 - β9) = 2 (α8 - β8)
⇒ a10 - 6a9 =2a9 ⇒
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