Question

hloo guys solve this problem fast please​

Answer 1

Answer:

$a {x}^{2} + bx + c = 0$

Roots,

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

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

As per the question

$\frac{1}{ {( \alpha + b)}^{2} } + \frac{1}{ {( \beta - b)}^{2} }$

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

Squaring

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

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