View Single Post
Dec11-09, 05:26 AM
P: 33

Given a1+a2+a3+...+an=0 and a1^2+a2^2+...+an^2=1, (all real numbers)

find the maximal value of a1*a2+a2*a3+...+an*a1

Thoughts so far:

I've treated the expression as a combination of n variables and differentiated - when it came to putting the constraints in it got to be a hideous mess.

It is easily factorisable as 0.5*( (a1+a2)^2 + (a2+a3)^2 +...+ (an+a1)^2 ) -1, but then maximising the inside is just as hard.

Help would be appreciated! (Also, sorry about the lack of LATEX knowhow).
Phys.Org News Partner Science news on
Law changed to allow 'unlocking' cellphones
Microsoft sues Samsung alleging contract breach
Best evidence yet for coronal heating theory detected by NASA sounding rocket