Let `x` be the arithmetic mean and `y ,z` be the two geometric means between any two positive numbers, then `(y^3+z^3)/(x y z)=dot` (1997C, 2M)

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

If a be the arithmetic mean and b, c be the two geometric means between any two positive numbers, then (b^3 + c^3) / abc equals

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

The arithmetic mean of two numbers x and y is 3 and geometric mean is 1. Then x^(2)+y^(2) is equal to

The geometric mean of x and y is 6 and the geometric mean of x, y and z is also 6. Then the value of z is

If x,y,z are distinct positive numbers,then prove that (x+y)(y+z)(z+x)>8xyz

If x, y, z are in arithmetic progression and a is the arithmetic mean of x and y and b is the arithmetic mean of y and z, then prove that y is the arithmetic mean of a and b.

If x,y,z are in A.P.and A1 is the arithmetic mean of x,y and A2 is the arithmetic mean of y,z then prove that the arithmetic mean of A1 and A2 isy

If x, y, z are positive real numbers such that x+y+z=a, then