α, β are the roots of x2−10x−8=0 with α > β. If an = αn - βn for n∈ N , then the value of a10 - 8a85a9 is

an= αn- βnx2−10x−8=0a10-8a85a9=α10-β10 - 8 α8-β85a9= α8α2-8- β8β2-85a9= α810α- β810β5a9= 10α9-β95α9-β9= 2

α, β are the roots of x2−10x−8=0 with α > β. If an = αn - βn for n∈ N , then the value of a10 - 8a85a9 is

an= αn- βnx2−10x−8=0a10-8a85a9=α10-β10 - 8 α8-β85a9= α8α2-8- β8β2-85a9= α810α- β810β5a9= 10α9-β95α9-β9= 2

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$α, β$ are the roots of $x^{2} - 10 x - 8 = 0$ with $α > β$ . If $a_{n} = α^{n} - β^{n}$ for $n \in N$ , then the value of $\frac{a_{10} - 8 a_{8}}{5 a_{9}}$ is

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$a_{n} {= α}^{n} {- β}^{n}$

$x^{2} - 10 x - 8 = 0$

$\frac{a_{10} {-8a}_{8}}{{5a}_{9}} = \frac{(α^{10} {-β}^{10}) - 8 (α^{8} {-β}^{8})}{{5a}_{9}}$

$= \frac{α^{8} (α^{2} -8) {- β}^{8} (β^{2} -8)}{{5a}_{9}}$

$= \frac{α^{8} (10α) {- β}^{8} (10β)}{{5a}_{9}}$

$= \frac{10 (α^{9} {-β}^{9})}{5 (α^{9} {-β}^{9})} = 2$

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α, β are the roots of x2−10x−8=0 with α > β. If an = αn - βn for n∈ N , then the value of a10 - 8a85a9 is

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$α, β$ are the roots of $x^{2} - 10 x - 8 = 0$ with $α > β$ . If $a_{n} = α^{n} - β^{n}$ for $n \in N$ , then the value of $\frac{a_{10} - 8 a_{8}}{5 a_{9}}$ is