Our textbook has no knowledge about a hyper-surface (or the word is mixed into a random paragraph which I will never find), so I could use some help with this one. I have a potential answer for the second half of this question, which boils down to the AM-GM Inequality, but I'm not sure if my answer is what is being asked for (the context of the question is a bit vague to me).
Find the minimum distance from the origin to a point on the hyper-surface
I've been told by another source that, since a hyper-surface is a surface of dimensions, the minimum distance would occur along the line , which would mean when they all equal . However, showing this is proving difficult for me.
Deduce that, for ,
with equality occurring only when all of the 's are equal.
(HINT: look at )
For this second half, this is basically the inequality of arithmetic and geometric means (or the AM-GM inequality), for which I could easily find a proof. However, due to how the question is worded, I'm not entirely sure if a proof is what is being asked of us. As such, I could use some clarification.
Any help on this one would be appreciated.