If a = 925, b = 924, c = 923, then find a2 + b2 + c2 - ab - bc - ca.

2 3 12 5

3

a2 + b2 + c2 - ab - bc - ca = \(\frac{1}{2}\) [(a - b)2 + (b - c)2 + (c - a)2]                                        = \(\frac{1}{2}\) [(925 - 924)2 + (924 - 923)2 + (923 - 925)2]                                        = \(\frac{1}{2}\) [1 + 1 + 4] = 3