(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello all. The question asked here is to find the point on the surface:

z^{2}- xy = 1

that is closest to the origin.

3. The attempt at a solution

I only have experience in doing this with 2 variables. I begin by trying to find "d", I get that d = sqrt[...] but I have three variables to deal with. I end up with

d^{2}= (z^{2}-1)/y + (z^{2}-1)/x + xy + 1

The problem is that the partial derivatives with respect to x, y and z are quite messy and they don't look right... Does this look correct so far? Thanks all!

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# Point on surface closest to origin.

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