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

,

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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

)

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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.