Problem

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2017

Tags: equation, algebra, roots



If $a$ is real number such that $x_1$ and $x_2$, $x_1\neq x_2$ , are real numbers and roots of equation $x_2-x+a=0$. Prove that $\mid {x_1}^2-{x_2}^2 \mid =1$ iff $\mid {x_1}^3-{x_2}^3 \mid =1$