`x,y,z` be positive numbers, show that `(x + y + z)^3 >= 27 xyz.`

x,y,z be positive numbers,show that (x+y+z)^(3)>=27xyz

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

Let A=[(x,y,z),(y,z,x),(z,x,y)] , where x, y and z are real numbers such that x + y + z > 0 and xyz = 2 . If A^(2) = I_(3) , then the value of x^(3)+y^(3)+z^(3) is__________.

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

If x,y,z are positive real numbers such that y,z,x are in G.P. and x+y+z=xyz then the maximum value of equals (76)/(x^(4)+x^(2)+7) equals

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

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 and z are positive real numbers such that x=(12-yz)/(y+z) the maximum value of xyz=