If x = 2015, y = 2014, z = 2013, then the value of x² + y² + z² - xy - yz - zx is?

Solution (By Examveda Team)

$$\eqalign{ & x = 2015 \cr & y = 2014 \cr & z = 2013 \cr & \therefore {x^2} + {y^2} + {z^2} - xy - yz - zx \cr & = \frac{1}{2}\left[ {{{\left( {x - y} \right)}^2} + {{\left( {y - z} \right)}^2} + {{\left( {z - x} \right)}^2}} \right] \cr & = \frac{1}{2}\left[ {{{\left( {2015 - 2014} \right)}^2} + {{\left( {2014 - 2013} \right)}^2} + {{\left( {2013 - 2015} \right)}^2}} \right] \cr & = \frac{1}{2}\left( {1 + 1 + 4} \right) \cr & = 3 \cr} $$