Question

If (x/y) = (6/5), find the value (x2+y2)/(x2-y2)

Answer 1

x/y=6
x=6y/5
(x2+y2)/(x2-y2)=(36y2/25+y2)/(36y2/25-y2)
=61/11

Answer 2

Answer:

Value of $\frac{x^{2}+y^{2}}{x^{2}-y^{2}}$ = $\frac{61}{11}$

Explanation:

Given $\frac{x}{y}=\frac{6}{5}$ ---(1)

$\implies \left(\frac{x}{y}\right)^{2}=\left(\frac{6}{5}\right)^{2}$

$\implies \left(\frac{x}{y}\right)^{2}=\frac{36}{25}$ ---(2)

Now ,

Value of $\frac{x^{2}+y^{2}}{x^{2}-y^{2}}$

Divide numerator and denominator by y² , we get

=$\frac{\frac{x^{2}}{y^{2}}+\frac{y^{2}}{y^{2}}}{\frac{x^{2}}{y^{2}}-\frac{y^{2}}{y^{2}}}$

= $\frac{\left(\frac{x}{y}\right)^{2}+1}{\left(\frac{x}{y}\right)^{2}-1}$

= $\frac{\frac{36}{25}+1}{\frac{36}{25}-1}$

/* from (2) */

= $\frac{\frac{(36+25)}{25}}{\frac{36-25}{25}}$

= $\frac{\frac{61}{25}}{\frac{11}{25}}$

After cancellation, we get

= $\frac{61}{11}$

Therefore,

Value of $\frac{x^{2}+y^{2}}{x^{2}-y^{2}}$ = $\frac{61}{11}$

•••••