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Ok this is the question I had on a test today:

given this constraint equation z^2-xy+1=0 find the min. distance from the origin using Lagrange method.

so basically you use D^2=x^2+y^2+z^2 as the other equation. however, it basically goes nuts from there. especially if you set it up like you are suppose to.

Fx=(lambda)Gx

Fy=(lambda)Gy

Fz=(lambda)Gz

g=0

(capitals are partial derivatives)

with f as the distance formual and g as the constraint

this one sucks but if someone could help it would be greatly appreciated

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# Crazy lagrange problem

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