Let α>β be the roots of x²-6x-2=0 and an=αⁿ-βⁿ (n 1). Then a₁₀-2a₈ 2a₉ is (a) 1 (b) 2 (c) 3 (d) 4

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[JEE Advanced 2011] let alpha beta be the roots of x 2 6x 2 0 and a

VAVidaara Admin Asked 2d ago 0 views 1 answer

Let $\alpha>\beta$ be the roots of $x^2-6x-2=0$ and $a_n=\alpha^n-\beta^n$ ($n\ge1$). Then $\dfrac{a_{10}-2a_8}{2a_9}$ is

(a) $1$
(b) $2$
(c) $3$
(d) $4$

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

Correct answer: (c) $3$

From $x^2=6x+2$, $a_n=6a_{n-1}+2a_{n-2}$, so $a_{10}-2a_8=6a_9$ and the ratio is $3$.

JEE Advanced 2011 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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