Question

Find the third proportional to a – b and a² – b²

Answer 1

Let the third proportional to a – b and a² – b² be x.

`=>` a – b, a² – b², x are in continued proportion.

`=>` a – b : a² – b² = a² – b² : x

`=> (a - b)/(a^2 - b^2) = (a^2 - b^2)/x`

`=> x = (a^2 - b^2)^2/(a - b)`

`=> x = ((a + b)(a - b)(a^2 - b^2))/(a - b)`

`=>` x = (a + b)(a² – b²)