If a = 2017, b = 2016, c = 2015, then

find a² + b² + c² - ab - bc - ca.

3

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

                                       = \(\frac{1}{2}\) [(2017 - 2016)² + (2016 - 2015)² + (2015 - 2017)²]

                                       = \(\frac{1}{2}\) [1 + 1 + 4] = 3