Question:(adsbygoogle = window.adsbygoogle || []).push({});

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).

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Maximise this quadaratic form, subject to these constraints.

**Physics Forums | Science Articles, Homework Help, Discussion**