In `Inx+Iny + Inz =1`, then the minimum value of `e^(-1/3) (x+y+ z)` is

In In x+In y+In z=1, then the minimum value of e^(-(1)/(3))(x+y+z) is

The minimum value of |z-1|+|z-3| is

If xyz=(1-x)(1-y)(1-z) Where 0<=x,y, z<=1 , then the minimum value of x(1-z)+y (1-x)+ z(1-y) is

If xyz=(1-x)(1-y)(1-z) Where 0<=x,y,z<=1, then the minimum value of x(1-z)+y(1-x)+z(1-y) is

If x, y, z are non-negative real numbers satisfying x+y+z=1 , then the minimum value of ((1)/(x)+1)((1)/(y)+1)((1)/(z)+1) , is

If x, y, z are non-negative real numbers satisfying x+y+z=1 , then the minimum value of ((1)/(x)+1)((1)/(y)+1)((1)/(z)+1) , is

Find the minimum value of |z-1 if |z-3|-|z+1||=2

If xyz = 1 and x, y, z gt 0 then the minimum value of the expression (x+2y)(y+2z)(z+2x) is

If xyz = 1 and x, y, z gt 0 then the minimum value of the expression (x+2y)(y+2z)(z+2x) is

If x=3, y=2 and z=-1 , then the value of (x^3+y^3+1)/(y^3-z^3) is