Question

Hello, can u plzz give my questions? ​

Answer 1

$\textbf{Answer is in Attachment !}$

Answer 2

Given alpha and beta are the roots of equation, so x= alpha and x= beta.

x^2 -6x -2 = 0

${ \alpha }^{2} - 6 \alpha - 2 = 0$

Taking -6 alpha on other side

so,

${ \alpha }^{2} - 2 = 6 \alpha$

-------(1)

x^2 -6x -2 =0

${ \beta }^{2} - 6 \beta - 2 = 0$

${ \beta }^{2} - 2 = 6 \beta$

-------(2)

Now a10-2a8 /2a9

$\frac{\alpha 10 - \beta 10 - 2( \alpha 8 - \beta 8)}{2 \alpha 9 - \beta 9}$

$\frac{ \alpha 10 - \beta 10 - 2 \alpha 8 + 2 \beta 8}{2 (\alpha 9 - \beta 9)}$

$\frac{ \alpha 10 - 2 \alpha 8 - \beta 10 + 2 \beta 8}{2( \alpha 9 - \beta 9)}$

Taking alpha 8 and beta 8 common

$\frac{ \alpha {}^ 8( \alpha {}^{2} - 2) - \beta {}^{8}( { \beta }^{2} - 2) }{2 \alpha {}^{9} - \beta {}^{9} }$

$\frac{ { \alpha }^{8}6 \alpha - \beta {}^{8} 6 \beta }{2 (\alpha {}^{9} - \beta {}^{9} ) }$

$\frac{6( { \alpha }^{9} - { { \beta }^{9}) } }{2( { \alpha }^{9} - { \beta }^{9} )}$

= 3

So, option C is the correct answer .