If x : y = 4:3, then find the value of $$\frac{x^2 + y^2}{x^2 - y^2}$$​

Correct option is A

​$$\textbf{Given:} \quad x : y = 4 : 3 \\\Rightarrow x = 4k, \quad y = 3k \\[10pt]\text{Now, compute the required ratio:} \\\frac{x^2 + y^2}{x^2 - y^2}= \frac{(4k)^2 + (3k)^2}{(4k)^2 - (3k)^2}= \frac{16k^2 + 9k^2}{16k^2 - 9k^2}= \frac{25k^2}{7k^2}= \frac{25}{7} \\[10pt]\therefore (x^2 + y^2) : (x^2 - y^2) = \boxed{25 : 7}$$​​