I was given the two equations f=x^2y^2z^2 and x^2+y^2+z^2=1

(I'll use 'u' to be equal to lambda)

and then set up my equations to be x^2y^2z^2-ux^2-uy^2-uz^2+u

taking the partial derivatives I got

fx=2x*y^2*z^2-2ux+1=0

fy=2x^2*y*z^2-2uy+1=0

fz=2x^2*y^2*z-2uz+1=0

fu=-x^2-y^2-z^2+1=0

I cant seem to find a way to solve this system of equations, can anyone? Or tell me what I did wrong?

Thanks!