Proportion...

Hello snigdha

Quote:

Originally Posted by snigdha

Find the Mean Proportion:
(a+b)* (a-b)^3 , (a+b)^3 *(a-b)

The Mean Proportion of two numbers is, I think, what is more usually called the Geometric Mean, and is the square root of their product. So if $b$ is the mean proportion of $a$ and $c$ , then
$b^2 = ac$ or $b = \sqrt{ac}$

So here the mean proportion is
$\sqrt{(a+b)(a-b)^3(a+b)^3(a-b)}$
$=\sqrt{(a+b)^4(a-b)^4}$

$=(a+b)^2(a-b)^2$

which could be written as

$=(a^2-b^2)^2$
Grandad