Question

Find the mean proportional between a - b and a³ - a²b

Answer 1

The mean proportional of two numbers is the same as the geometric mean of the the two numbers.

Geometric mean of two numbers x and y = $\sqrt{xy}$

So mean proportional of a - b and a³ - a²b is 

$=\sqrt{(a-b)(a^3-a^2b)} \\= \sqrt{(a-b)*a^2(a-b)}\\ = \sqrt{a^2*(a-b)^2} \\=\boxed{a(a-b)}$

Answer 2

Step-by-step explanation:

The mean proportional of two numbers is the same as the geometric mean of the the two numbers.

Geometric mean of two numbers x and y = \sqrt{xy}

xy

So mean proportional of a - b and a³ - a²b is

$$\begin{lgathered}=\sqrt{(a-b)(a^3-a^2b)} \\= \sqrt{(a-b)*a^2(a-b)}\\ = \sqrt{a^2*(a-b)^2} \\=\boxed{a(a-b)}\end{lgathered}$$