The subduplicate ratio of $(x^{2} - y^{2})^{2} : (x + y)^{2}$ is _____

x^{2} - y^{2} : 1

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x - y : 1

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x + y : 1

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1 : x + y

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Solution

The correct option is B $x - y : 1$
$\frac{(x^{2} - y^{2})^{2}}{(x + y)^{2}} = \frac{((x - y) (x + y))^{2}}{(x + y)^{2}} = \frac{(x - y)^{2}}{1}$
$∴$ The subduplicate ratio of $(x - y)^{2} : 1$ is $\sqrt{(x - y)^{2}} : \sqrt{1} = (x - y) : 1$ .

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The subduplicate ratio of (x2−y2)2:(x+y)2 is _____

The correct option is B x−y:1(x2−y2)2(x+y)2=((x−y)(x+y))2(x+y)2=(x−y)21∴ The subduplicate ratio of (x−y)2:1 is √(x−y)2:√1=(x−y):1.

The subduplicate ratio of $(x^{2} - y^{2})^{2} : (x + y)^{2}$ is _____

The correct option is B $x - y : 1$
$\frac{(x^{2} - y^{2})^{2}}{(x + y)^{2}} = \frac{((x - y) (x + y))^{2}}{(x + y)^{2}} = \frac{(x - y)^{2}}{1}$
$∴$ The subduplicate ratio of $(x - y)^{2} : 1$ is $\sqrt{(x - y)^{2}} : \sqrt{1} = (x - y) : 1$ .