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

If x, y, z are distinct positive numbers such that x+(1)/(y)=y+(1)/(z)=z+(1)/(x) , then the value of xyz is __________

If x, y, z are distinct positive numbers such that x+(1)/(y)=y+(1)/(z)=z+(1)/(x) , then the value of xyz is __________

If x, y, z are all positive real numbers, then prove that, If x+y+z=1 , then prove that (1-x)(1-y)(1-z)ge8xyz .

If x,y,z are positive real numbers, prove that: sqrt(x^-1 y).sqrt(y^-1z).sqrt(z^(-1)x)=1

If x,y,z are positive distinct integers, then (x+y) (y+z) (z+x), is

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

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

If x,y,z, are real and distinct number, then the value of ((x-y)^3+(y-z)^3+(z-x)^2)/((x-y)(y-z)(z-y)) is