if `x+1/y=1` and `y+1/z=1` then the value of `z+1/x`

If x+1/y =1 and y + 1/z =1 then find the value of z + 1/x

If x+y+z=1,x y+y z+z x=-1 and x y z=-1, find the value of x^3+y^3+z^3dot

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 be greater than 1, then the value of |{:(1, log_(x)y, log_(x) z),(log_(y)x , 1 ,log_(y)z),(log_(z)x , log_z y , 1 ):}| =

If x, y and z be greater than 1, then the value of |(1,log_(x)y,log_(x)z),(log_(y)x,1,log_(y)z),(log_(z)x,log_(z)y,1)| is

If x+y+z=1,\ x y+y z+z x=-1\ \ a n d\ x y z=-1, find the value of x^3+y^3+z^3