Sum of cross terms vs sum of squares? What do we know about sum of squares vs sum of cross terms? Does one always dominate the other? Any theorems on that?
e.g
for  
$a^2 + b^2 + c^2 \ < ? > \ ab + ac + bc $
for any number of terms.
Thank you

for $a,b,c\in R(a\neq b\neq c)$
$(a-b)^2+(b-c)^2+(c-a)^2>0$
$a^2+b^2+c^2>ab+bc+ca$
