Question

Find the third proportional to (x² – y²) and (x + y) .

Answer 1

Let the third proportional to (x² – y²) and (x + y) be A. Then 

(x² – y²) : (x + y) : : (x + y) : A 

⇒ (x² – y²) x A = (x + y)² ⇒ A = \(\frac{(x+y)^2}{x^2-y^2}\)

⇒ A = \(\frac{(x+y)^2}{(x+y)(x-y)}\) = \(\frac{x+y}{x-y}.\)