Use lagrange multipliers to find the shortest distance

[anubis01]

Homework Statement

Use lagrange multipliers to find the shortest distance between a point on the elliptic paraboloid z=x^2 +y^2

Homework Equations

The Attempt at a Solution

http://img716.imageshack.us/img716/7272/cci1902201000000.jpg

I'm not that good with using the equation editor, so I scanned my work.

I'm stuck on the last part where I'm trying to factor the equation to find a solution for $$\lambda$$, I can't seem to find a solution that would make the equation zero, which is what i need in order to do the long division to factor that equation.

 

[Dick]

Your constraint is x^2+y^2-z=0. You differentiate lambda*(x^2+y^2-z). So you have a mistake on step 3. The d/dz equation should be 2*(z-1/2)=(-lambda). That may be why you are having a hard time with the resulting equation.

 

[anubis01]

ah, now the equation makes much more sense, thanks for the help.