The third proportional to -x-2- - y-2- and -x - y- is-x-y-displaystyle frac -x - y-x - y-displaystyle frac -x - y-x - y-x-2- - y-2-

Question

Toppr Admin · Accepted Answer

Let third proportional is x-x2-x2212-y2-x-x2212-y-x-x2212-y-x-x21D2-x-x-x2212-y-x-x2212-y-x2-x2212-y2-x21D2-x-x-x2212-y-x-x2212-y-x-y-x-x2212-y-x21D2-x-x-x2212-y-x-y-xA0-

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

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

The third proportional to (x2−y2) and (x−y) is(x+y)x+yx−yx−yx+y(x2−y2)

Let third proportional is x(x2−y2):(x−y)=(x−y):x⇒x=(x−y)(x−y)(x2−y2)⇒x=(x−y)(x−y)(x+y)(x−y)⇒x=(x−y)(x+y)

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

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