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.`

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 the two geometric means between any two positive numbers. Then, value of (y^3+z^3)/xyz ​=?

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

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

If x+y+z=0 show that x^3+y^3+z^3=3x y z .

If y is the mean proportional between x and z, prove that : (x^(2) - y^(2) + z^(2))/(x^(-2) - y^(-2) + z^(-2)) = y^(4) .

If x,y and z are three different numbers, then prove that : x^(2) + y^(2) + z^(2)- xy - yz- zx is always positive

Using properties of determinants, prove that |(a+x, y, z),(x, a+y, z),(x, y,a+z)|=a^2(a+x+y+z)

If x. y, z are positive real numbers such that x^2+y^2+z^2=27, then x^3+y^3+z^3 has