Question

Find the mean proportion of (a-b) & (a^3-a^2b), a>b​

Answer 1

Answer:

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 = √ xy

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

= √ ( a-b) ( a³- a²b)

= √ (a-b) *a²(a-b)

= √a²* ( a-b)²

= a( a- b)

Hope it helps you...

Answer 2

Answer:

The mean proportion of the given two numbers can be given by finding their Geometric Mean(G.M) (both are same),

So,Geometric Mean(G.M) of the given two numbers=$\sqrt{xy}$

G.M=$\sqrt{(a-b)(a^3-a^2b)}$

      =$\sqrt{(a-b).a^2(a-b)}$

      =$\sqrt{a^2(a-b)^2}$

      =${a(a-b)}$

∴The mean proportion of given numbers⇒${a(a-b)}$,where a>b

Hope it helps you.