Question

how to solve this question ​

Answer 1

$\huge\mathfrak{solution}$

Given:

$\bold{ \alpha \: and \: \beta are \: the \: roots \: of \:} \\ \bold{ {x}^{2} = x + 1}$

To find :

$\frac{ { \alpha }^{2} }{ \beta } - \frac{ { \beta }^{2} }{ \alpha }$

Here :

p(x) = x^2-x-1=0

•a= 1 •b=-1 and c=-1

As we know that:

$\alpha + \beta = - \frac{b}{a} = - ( \frac{ - 1}{1} ) = 1$

and

$\alpha \beta = \frac{c}{a} = \frac{ - 1}{1} = 1$

$\star \: \frac{ { \alpha }^{2} }{ \beta } - \frac{ { \beta }^{2} }{ \alpha } \\ \\ \star \frac{ { \alpha }^{3} - { \beta }^{3} }{ \alpha \beta }$

$\star \: \frac{ {( \alpha - \beta )}^{3} + 3 \alpha \beta ( \alpha - \beta ) }{ \alpha \beta }$

$\star \: ( \alpha - \beta ) \frac{( { \alpha - \beta )}^{2} + 3\alpha \beta }{ \alpha \beta }$

Option D is correct

$\boxed{ \red{- 2 \sqrt{5} }}$

Now , solution refer to the attachment

Answer 2

Answer:

OPTION=A

Step-by-step explanation:

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