JBMO-SL 2021 N2

The real numbers $x, y$ and $z$ are such that $x^2 + y^2 + z^2 = 1$ . a) Determine the smallest and the largest possible values of $xy + yz - xz$ . b) Prove that there does not exist a triple $(x, y, z)$ of rational numbers, which attains any of the two values in a).