Paul
Posts:
620
Registered:
7/12/10


Re: proof of an inequality
Posted:
Apr 23, 2013 3:14 PM


On Tuesday, April 23, 2013 5:11:14 PM UTC+1, oercim wrote: > Okey, I guess I got it. Let n=2, > > > > x1^2+x2^2>=((x1+x2)^2)/4 > > > > ==>4(x1^2+x2^2)>=(x1+x2)^2 > > ==>3(x1^2+x2^2)>=2x1x2 > > > > if x1=x2, it is obvious it holds, > > > > if x1 is not equal x2, then one is greater than other . Let say x1>x2 > > > > Then x1^2>x1x2. I guess it is easy to apply n variable case. Thanks alot.
I'm not sure whether you're getting there or not. I'll give two further hints for a cleaner solution. 1) Replace x^2 by a simpler function. 2) Think of the relationship between max and mean.
Paul

