# Math Help - problem with an inequality

1. ## problem with an inequality

I have seen a theorem:
If a1,a2,........,an are n positive numbers such that all are not equal, and m is any rational number not equal to 1 and 0,
then
{(a1+a2+........+an)/n}m ≤ or ≥ {(a1m+a2m+........+anm)/n} according as m doesn't or does lie between 0 and 1

I can't find out, when do they get equal?

2. ## Re: problem with an inequality

Just off the top of my head, but since the change from $\le$ to $\ge$, and vice-versa, occurs at 0 and 1, I would guess that the only places we could have "=" would be at 0 or 1 or both.