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Q.

Let α, β are the roots of x²- 6x - 2 = 0, if a_n= αⁿ- βⁿ for n ≥ 1, then the value of $\frac{a_{10} - 2 a_{8}}{2 a_{9}} =$

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a

-3

b

-6

c

6

d

3

answer is D.

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Detailed Solution

$\begin{array}{l} α^{2} - 2 = 6 α \Rightarrow α^{10} - 2 α^{8} = 6 α^{9} \to (1) \\ β^{10} - 2 β^{8} = 6 β^{9} \to (2) \end{array}$

Now (1) – (2)

$\Rightarrow a_{10} - 2 a_{8} = 6 a_{9} \Rightarrow \frac{a_{10} - 2 a_{8}}{2 a_{9}} = 3$

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