Question

find the value of a( alpha²/beta + beta²/alpha)+ b( alpha/beta + beta³/alpha). The value of alpha + beta = -b/a , alpha × beta = c/a
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Answer 1

Answer:

Given

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

and

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

Given expression :

$a( \frac{ { \alpha }^{2} }{ \beta } + \frac{ { \beta }^{2} }{ \alpha } ) + b( \frac{ { \alpha }^{3} }{ \beta } + \frac{ { \beta }^{3} }{ \alpha } )$

Now,

$a({ \alpha }^{3} + { \beta }^{3 } ) = a{( (\alpha + \beta )}^{3} - 3 \alpha \beta )\\ = a({( - \frac{b}{a}}) ^{3} - 3( \frac{c}{a} ) )= a( - \frac{ {b}^{3} }{ {a}^{3} } - \frac{3c}{a} ) \\ = a(\frac{ - {b}^{3} - 3 {a}^{2}c }{ {a}^{3} } ) = \frac{ - {b}^{3} - 3 {a}^{2}c }{ {a}^{2} }$

Again,

#rb3305

Step-by-step explanation:

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