#### Question

Find the third proportional to a^{2} – b^{2} and a + b.

#### Solution

Let the third proportional to `a^2 - b^2` and a + b be n

`=> a^2 - b^2, a + b` and n are in continued proportion

`=> a^2 - b^2 : a + b = a _ b : n`

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

Is there an error in this question or solution?

Solution Find The Third Proportional to A2 – B2 And a + B. Concept: Proportions.