If a = 1021, b = 1020, c = 1018, then

find a² + b² + c² - ab - bc - ca.

7

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

                                       = \(\frac{1}{2}\) [(1021 - 1020)² + (1020 - 1018 )² + (1018 - 1021)²]

                                       = \(\frac{1}{2}\) [1 + 4 + 9] = 7