Re: Inequality

From: georgesZ (zellerg_at_wanadoo.fr)
Date: 01/23/05 

Date: Sun, 23 Jan 2005 19:00:11 +0000 (UTC)

Thank you George,

Indeed what I asked is not true!
Your example prove it is false for n=10.

I just had a look back to my proof for n=4 and I found a mistake!

The polynomial P(x,y,z) which must be >=0, for x,y,z in R*+,
has value P(2, 0.1, 0.01)= -.88843992!!
(I said P(x,0,z)=x^3*z+1 but it is P(x,0,z)=x^3*z-x+1).

So, only for n=2 or 3, it is true that , for x1,x2,..,xn in R*+ we have
(x1+..+xn)/(x1*..*xn)^(1/n) <= x1/x2+..+xn/x1.

Best regards,
Georges