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,x gt 0 and x+y+z=1 then (xyz)/((1-x) (1-y) (1-z)) is necessarily.

If x,y,x gt 0 and x+y+z=1 then (xyz)/((1-x) (1-y) (1-z)) is necessarily.

If xy + yz + zx = 1 , prove that : x/(1-x^2)+y/(1-y^2)+z/(1-z^2)= (4xyz)/((1-x^2)(1-y^2)(1-z^2)) .

If x+y+z=xyz , prove that x/(1-x^2)+ y/(1-y^2)+z/(1-z^2) =(4xyz)/((1-x^2)(1-y^2)(1-z^2))

If (xyz)^(x+y+z)=1 where xyz!=1 and log_(3)(xyz)=-1, then log_(xyy)(x^(3)+y^(3)+z^(3)) equals

If x+y+z=xyz then show that (2x)/(1-x^(2))+(2y)/(1-y^(2))+(2z)/(1-z^(2))=(8xyz)/((1-x^(2))(1-y^(2))(1-z^(2)))

If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= 4xyz/((1-x^(2))(1-y^(2)) (1-z^(2)))

If xy+yz+xz=1, then prove that (x)/(1-x^(2))+(y)/(1-y^(2))+(z)/(1-z^(2))=(4xyz)/((1-x^(2))(1-y^(2))(1-z^(2)))

If xy+yz+zx=1 show that (x)/(1-x^(2))+(y)/(1-y^(2))+(z)/(1-z^(2))=(4xyz)/((1-x^(2))(1-y^(2))(1-z^(2)))

if x+y+z=0,then Prove that (xyz)/((x+y)(y+z)(z+x))=-1 where(x!=-y,y!=-z,z!=-x)