If the sum of the squares of nonnegative real numbers a,b, and c is 13, and ab + bc + ca = 6, then what is the sum of a,b, and c?

a^2 + b^2 + c^2  = 13

ab + bc + ca = 6

Just by inspection....an integer solution is  a = 0, b = 2   and c = 3

So

0^2 + 2^2 + 3^2 =   13

And

0*2 + 2*3  + 3*0   =   6

And their sum = 5

Another possible integer  solution is  (a, b, c) =   (0, 3, 2 )