Find the third proportional to: x - y, x^2- y^2 - Vidyadip

Question

Find the third proportional to:
$x - y, x^2- y^2$

✓

Answer

Let A be the third proportional then
$( x - y ):\left( x ^2- y ^2\right)=\left( x ^2- y ^2\right): A $
$ \Rightarrow \frac{x-y}{x^2-y^2}=\frac{x^2-y^2}{ A }$
$ \Rightarrow A =\frac{\left(x^2-y^2\right)}{x-y} $
$ \Rightarrow A =( x + y )\left( x ^2- y ^2\right) .$

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