Why does losing solutions happen with nonlinear systems in Lagrange multipliers?

[ice109]

so I'm doing these lagrangian multipliers in calc class and it involves nonlinear systems and apparently the techniques I'm used to applying to linear systems aren't appropriate because i keep losing solutions, getting the wrong ones etc.

so yea what are some efficient algorithms for this

 

[Hurkyl]

Never divide by something that might be zero. Split into cases when necessary.


Aside from that advice, it might help if you give an example of your work that leads to missing or wrong solutions.

 

[ice109]

i just have to be rigorous