If a = 7, b = 5 and c = 3, then the value of a² + b² + c² - ab - bc - ca is?

Solution (By Examveda Team)

$$\eqalign{ & {a^2} + {b^2} + {c^2} - ab - bc - ca \cr & = \frac{1}{2}\left[ {{{\left( {a - b} \right)}^2} + {{\left( {b - c} \right)}^2} + {{\left( {c - a} \right)}^2}} \right] \cr & = \frac{1}{2}\left[ {{{\left( {7 - 5} \right)}^2} + {{\left( {5 - 3} \right)}^2} + {{\left( {3 - 7} \right)}^2}} \right] \cr & = \frac{1}{2}\left( {4 + 4 + 16} \right) \cr & = \frac{{24}}{2} \cr & = 12 \cr} $$