Let α,β be the roots of x2−6x−2=0 with α>β. If an=αn−βn for n≥1 then the value of a10−2a82a9 is

α+β=6,αβ=−2a10−2a82a9=(α10−β10)−2(α8−β8)2(α9−β9)(α9−β9)(α+β)2(α9−β9)=62=3

Let α,β be the roots of x2−6x−2=0 with α>β. If an=αn−βn for n≥1 then the value of a10−2a82a9 is

α+β=6,αβ=−2a10−2a82a9=(α10−β10)−2(α8−β8)2(α9−β9)(α9−β9)(α+β)2(α9−β9)=62=3

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Let $α, β$ be the roots of $x^{2} - 6 x - 2 = 0$ with $α > β .$ If $a_{n} = α^{n} - β^{n}$ for $n \geq 1$ then the value of $\frac{a_{10} - 2 a_{8}}{2 a_{9}}$ is

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$α + β = 6, α β = - 2$

$\frac{a_{10} - 2 a_{8}}{2 a_{9}} = \frac{(α^{10} - β^{10}) - 2 (α^{8} - β^{8})}{2 (α^{9} - β^{9})}$

$\frac{(α^{9} - β^{9}) (α + β)}{2 (α^{9} - β^{9})} = \frac{6}{2} = 3$

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Let α,β be the roots of x2−6x−2=0 with α>β. If an=αn−βn for n≥1 then the value of a10−2a82a9 is

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Let $α, β$ be the roots of $x^{2} - 6 x - 2 = 0$ with $α > β .$ If $a_{n} = α^{n} - β^{n}$ for $n \geq 1$ then the value of $\frac{a_{10} - 2 a_{8}}{2 a_{9}}$ is