If $(x : y)$ = 2:1, then $(x^{2} - y^{2}) : (x^{2} + y^{2})$ is :

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Solution

$\frac{x}{y} = \frac{2}{1}$ or $[\frac{x^{2}}{y^{2}} = \frac{2^{2}}{1} = \frac{(4 p)}{(1 p)} = \frac{(4)}{(1)}]$
$\to \frac{x^{2} - y^{2}}{x^{2} + y^{2}}$
$\Rightarrow x^{2} = 4, y^{2} = 1 p {x^{2} = 4 p y^{2} = 1 p}$
from above
So, $\frac{x^{2} - y^{2}}{x^{2} + y^{2}} \Rightarrow \frac{4 x - 1 x}{4 x + 1 x} [\frac{4 p - 1 p}{4 p + 1 p}]$
$= \frac{3 x}{5 x} = (\frac{3}{5})$
So, $\frac{x^{2} - y^{2}}{x^{2} + y^{2}} = \frac{3}{5}$

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