If a = 1044, b = 1043, c = 1042, then find a2 + b2 + c2 - ab - bc - ca.

0 2 6 3

3

a2 + b2 + c2 - ab - bc - ca = \(\frac{1}{2}\) [(a - b)2 + (b - c)2 + (c - a)2]                                        = \(\frac{1}{2}\) [(1044 - 1043)2 + (1043 - 1042 )2 + (1042 - 1044)2]                                        = \(\frac{1}{2}\) [1 + 1 + 4] = 3