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.`

Explanation

Let `a` and `b` are two positive numbers.

Then,

`x = (a+b)/2`

`y^2 = az and z^2 = yb`

`=>y^3 = ayz and z^3 = byz`

Now, `(y^3+z^3)/(xyz) = (ayz+byz)/(((a+b)/2)yz)`

`=2((a+b)yz)/((a+b)yz) =2`

`:. (y^3+z^3)/(xyz) = 2.`