The third proportional to $(x^{2} - y^{2})$ and $(x - y)$ is

(x + y)

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\frac{x + y}{x - y}

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\frac{x - y}{x + y}

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(x^{2} - y^{2})

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Solution

The correct option is C $\frac{x - y}{x + y}$
Let third proportional is x
$(x^{2} - y^{2}) : (x - y) = (x - y) : x$
$\Rightarrow x = \frac{(x - y) (x - y)}{(x^{2} - y^{2})}$
$\Rightarrow x = \frac{(x - y) (x - y)}{(x + y) (x - y)}$
$\Rightarrow x = \frac{(x - y)}{(x + y)}$

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The third proportional to $x^{2} - y^{2}$ and $(x - y)$ is :

The third proportion to $(x^{2} - y^{2})$ and (x - y), where x and y are unequal, is:

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(x^{2} - y^{2})

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\frac{x^{2} - y^{2}}{x^{2} + 2 x y + y^{2}} : \frac{x - y}{x + y}

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