Find the Mean Proportion:

(a+b)* (a-b)^3 , (a+b)^3 *(a-b)

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- Feb 25th 2010, 07:40 AMsnigdhaProportion...
Find the Mean Proportion:

(a+b)* (a-b)^3 , (a+b)^3 *(a-b) - Feb 25th 2010, 10:35 PMGrandad
Hello snigdhaThe 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 $\displaystyle b$ is the mean proportion of $\displaystyle a$ and $\displaystyle c$, then

$\displaystyle b^2 = ac$ or $\displaystyle b = \sqrt{ac}$So here the mean proportion is

$\displaystyle \sqrt{(a+b)(a-b)^3(a+b)^3(a-b)}$which could be written as$\displaystyle =\sqrt{(a+b)^4(a-b)^4}$

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

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