Geometric Mean#!#N Mean Between Two Numbers

If A is the arithmetic mean and p and q be two geometric means between two numbers a and b, then prove that : p^(3)+q^(3)=2pq " A"

If "x" is the single A.M and "y,z" be two geometric means between two numbers a and b , then y^(3)+z^(3) is equal to

G is the geometric mean and p and q are two arithmetic means between two numbers a and b, prove that : G^(2)=(2p-q)(2q-p)

If n geometric means are inserted between two quantities; then the product of n geometric means is the nth power of the single geometric mean between two quantities.

The arithmetic mean between two numbers is A and the geometric mean is G. Then these numbers are:

The arithmetic mean between two numbers is A and the geometric mean is G.Then these numbers are: