Question

If $\alpha$ and $\beta$ are the roots of the equation, $7 x^{2}-3 x-2=0,$ then the value of $\frac{\alpha}{1-\alpha^{2}}+\frac{\beta}{1-\beta^{2}}$ is equal to :

• A. $\frac{27}{16}$
• B. $\frac{1}{24}$
• C. $\frac{27}{32}$
• D. $\frac{3}{8}$

Answer 1

Answer: (A)

$7 x^{2}-3 x-2=0$
$\alpha+\beta=\frac{3}{7}$
$\alpha \beta=\frac{-2}{7}$
$=\frac{\alpha}{1-\alpha^{2}}+\frac{\beta}{1-\beta^{2}}=\frac{\alpha+\beta-\alpha \beta(\alpha+\beta)}{1-\alpha^{2}-\beta^{2}+\alpha^{2} \beta^{2}}$
$=\frac{\frac{3}{7}+\frac{2}{7}\left(\frac{3}{7}\right)}{1-(\alpha+\beta)^{2}+2 \alpha \beta+\alpha^{2} \beta^{2}}$
$=\frac{27}{16}$