Originally Posted by

**CaptainBlack** You form the Lagrangian:

$\displaystyle L(x,y,z,\lambda)=xyz + \lambda (x^2+2y^2+3z^2-6)$

Then your system of equations is:

$\displaystyle

\frac{\partial}{\partial x}L(x,y,z,\lambda)=0

$

$\displaystyle

\frac{\partial}{\partial y}L(x,y,z,\lambda)=0

$

$\displaystyle

\frac{\partial}{\partial z}L(x,y,z,\lambda)=0

$

$\displaystyle

\frac{\partial}{\partial \lambda}L(x,y,z,\lambda)=0

$

(the last of these is just the constraint equation)

Is that what you have tried to do?

RonL