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## Homework Statement

Show that the distance D from the origin of any point (x , y , z) lying on the plane x + y + z= 1 satisfies

D^2 + x^2 + y^2 +(x + y -1)^2 .

By considering partial derivatives, find the point that is closest to the origin. Prove that this distance is genuinely minimal.

## Homework Equations

## The Attempt at a Solution

I did the first part. Knowing Distance is D^2 = x^2 + y^2 + z^2 then by re-arranging x + y + z =1 to -z = x + y - 1.

z^2 = (-z)^2 = (x + y - 1)^2

D^2 = x^2 + y^2 + (x + y - 1)^2

Not sure how to do the next part. How does considering partial derivatives help me find a point closest to the origin?

Any help would be great.