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

5 : 13

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2 : 3

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3 : 2

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13 : 5

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Solution

The correct option is A $5 : 13$
$∵ \frac{x + y}{x - y} = \frac{5}{1}$
$\Rightarrow 5 x - 5 y = x + y$
$\Rightarrow 4 x = 6 y$
$∴ x = \frac{3}{2} y$
$∴ \frac{x^{2} - y^{2}}{x^{2} + y^{2}} = \frac{{(\begin{matrix} \frac{3}{2} y \end{matrix})}^{2} - y^{2}}{{(\begin{matrix} \frac{3}{2} y \end{matrix})}^{2} + y^{2}}$
$= \frac{\frac{9}{4} y^{2} - y^{2}}{\frac{9}{4} y^{2} + y^{2}} = \frac{\frac{5}{4} y^{2}}{\frac{13}{4} y^{2}}$
$= \frac{5}{13}$ i.e., $5 : 13$

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If (x+y):(x−y)=5:1, then the value of (x2−y2):(x2+y2) will be

The correct option is A 5:13∵x+yx−y=51⇒5x−5y=x+y⇒4x=6y∴x=32y∴x2−y2x2+y2=(32y)2−y2(32y)2+y2=94y2−y294y2+y2=54y2134y2=513 i.e., 5:13

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