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Closest point to the origin

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Find the closest point of the surface:
xy + xz + yz = 1 to the origin.
and
x^2 + y^2 - Z^2 = 1 to the origin.

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Solution Summary

The solution provides an example of finding the closest point of given surfaces to the origin.

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Find the closest point of the surface:
(1) xy + xz + yz = 1 to the origin.
Actually we want to find the minimum value of subject to the constraints.
We use Lagrange multiplier
(1) Let
(1)
(2)
...

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