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"`

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)

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 a is the arithmetic mean and g is the geometric mean of two numbers, then

Let x be the arithmetic mean and y, z be two geometric means between any two positive numbers. Then, prove that (y^(3) + z^(3))/(xyz) = 2 .

Let x be the arithmetic mean and y, z be two geometric means between any two positive numbers. Then, prove that (y^3+z^3)/(xyz)=2 .

Let x be the arithmetic mean and y,z be tow geometric means between any two positive numbers.Then,prove that (y^(3)+z^(3))/(xyz)=2

Let x be the arithmetic mean and y ,z be tow geometric means between any two positive numbers. Then, prove that (y^3+z^3)/(x y z)=2.

If one arithmetic mean A and two geometric means p, q be inserted between two given numbers, then prove that, (p^(2))/(q) + (q^(2))/(p) = 2A .