Question

Third proportional between a^2 -b^2 and (a+b)^2

Answer 1

third proportion is =(a+b)^3/a-b.

Answer 2

Answer:

Third proportional to $a^2-b^2$ and $(a+b)^2$ will be $\frac{(a+b)^3}{a-b}$

Step-by-step explanation:

If a, b, and c are in proportion

Then,
$\frac{a}{b} =\frac{b}{c}$
⇒ $b^2=ac$

Now, in the question, we have asked the third proportional to $a^2-b^2$ and $(a+b)^2$

Let the third proportional to $a^2-b^2$ and $(a+b)^2$ be $x$
⇒ $\frac{a^2-b^2}{(a+b)^2}= \frac{(a^+b)^2}{x}$
⇒ $x= \frac{(a+b)^2 (a+b)^2}{a^2-b^2}$
⇒ $x= \frac{(a+b)^2 (a+b)^2}{(a+b) (a-b)}$
⇒ $x= \frac{(a+b)^3}{a-b}$