Mathematics - Quadratic Equation Question with Solution | TestHub

Given$\alpha$and$\beta$are the roots of the equation,$7x^2-3x-2=0,$then

$\alpha +\beta =\frac{3}{7} ; \alpha \beta =-\frac{2}{7}$

Now 

$\frac{\alpha }{1-{\alpha }^2}+\frac{\beta }{1-{\beta }^2}=\frac{(\alpha +\beta )-\alpha \beta (\alpha +\beta )}{\left(1-{\alpha }^2\right)\left(1-{\beta }^2\right)}=\frac{(\alpha +\beta )-\alpha \beta (\alpha +\beta )}{1+(\alpha \beta {)}^2-\left({\alpha }^2+{\beta }^2\right)}$

$\Rightarrow \frac{(\alpha +\beta )-\alpha \beta (\alpha +\beta )}{1+(\alpha \beta {)}^2-(\alpha +\beta {)}^2+2\alpha \beta }=\frac{\frac{3}{7}+\frac{2}{7}\left(\frac{3}{7}\right)}{1+{\left(\frac{2}{7}\right)}^2-{\left(\frac{3}{7}\right)}^2-2\left(\frac{2}{7}\right)}=\frac{27}{16}$