Question

If $(x+y):(x-y)=5:1$, then the value of $(x^2-y^2):(x^2+y^2)$ will be

• A. $5:13$
• B. $2:3$
• C. $3:2$
• D. $13:5$

Answer 1

Answer: (A)

The correct option is A $5:13$
$\because \frac{x+y}{x-y}=\frac{5}{1}$
$\Rightarrow 5x-5y=x+y$
$\Rightarrow 4x=6y$
$\therefore x=\frac{3}{2}y$
$\therefore \frac{x^2-y^2}{x^2+y^2}=\frac{{\left(\begin{array}{c}\frac{3}{2}y\end{array}\right)}^2-y^2}{{\left(\begin{array}{c}\frac{3}{2}y\end{array}\right)}^2+y^2}$
$=\frac{\frac{9}{4}{y}^2-y^2}{\frac{9}{4}{y}^2+y^2}=\frac{\frac{5}{4}{y}^2}{\frac{13}{4}{y}^2}$
$=\frac{5}{13}$ i.e., $5:13$