Sorry if this isn't in quite the right place, but the question is a Linear Algebra question, even though I can't really relate it to linear algebra myself, bar the obvious quadratic form.

Let a1,a2,...,an be real numbers such that:

a1+a2+a3+...+an=0 and

a1^2+a2^2+a3^2+...+an^2=1 (In case notation is ambiguous, 'a one squared plus ... plus a en squared = 1')

Question:

What is the maximum value of a1*a2+a2*a3+...+an*a1?

I am completely stumped. No clue at all, not even how to begin (apart from treating all the a's as independent variables and differentiating, but that gives me a horrible mess when it comes to put in the constraints). Any help would be appreciated.

Also, sorry about lack of LATEX knowhow.