If $$(x+y):(x−y)=7:3$$​, then find $$(x^2+y^2):(x^2-y^2)$$​.

Correct option is C

Given:
​$$\frac{x + y}{x - y} = \frac{7}{3}$$​
Formula Used:
Componendo and Dividendo:

If $$\frac{a}{b} = \frac{c}{d},$$​ then $$\frac{a + b}{a - b} = \frac{c + d}{c - d}$$​​

Solution:
$$\frac{(x + y) + (x - y)}{(x + y) - (x - y)} = \frac{7 + 3}{7 - 3}$$​​

​$$\frac{2x}{2y} = \frac{10}{4}$$​​

​$$\frac{x}{y} = \frac{5}{2}$$​​
Let x = 5k and y = 2k for some constant ($$k \neq 0).$$​
$$x^2 + y^2 = (5k)^2 + (2k)^2 = 25k^2 + 4k^2 = 29k^2$$​

​$$x^2 - y^2 = (5k)^2 - (2k)^2 = 25k^2 - 4k^2 = 21k^2$$​
$$\frac{x^2 + y^2}{x^2 - y^2} = \frac{29k^2}{21k^2} = \frac{29}{21}$$​