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

Answer: Option A

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