Question: Maxima of the given equation

Let say, 

A= A1+A2+.....................+An

B=B1+B2+.....................+Bn,

C=C1+C2+.....................+Cn

And all the values of A1 to Cn may be both positive or Negative.

Then, how to program to find the Maximum Value of  (A^2+B^2+C^2+A.B+B.C+C.A)^(1/2).

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