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

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

Prove that sqrt(x^(-1)y)xxsqrt(y^(-1)z)xxsqrt(z^(-1)x)=1

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

Show : sqrt( x^-1y) times sqrt( y^-1z ) times sqrt( z^-1x) = 1

If x, y, z are distinct positive real numbers is A.P. then (1)/(sqrt(x)+sqrt(y)), (1)/(sqrt(z)+sqrt(x)), (1)/(sqrt(y)+sqrt(z)) are in

If x,y,z are positive the minimum value of (x(1+y)+y(1+2)+z(1+x))/(sqrt(xy)z) 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,yand z are positive real numbers,then the minimum value of (x)/(y)+(y)/(z)+(z)/(x) is: