Problem

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2015

Tags: algebra, system of equations



For real numbers $x$, $y$ and $z$, solve the system of equations: $$x^3+y^3=3y+3z+4$$$$y^3+z^3=3z+3x+4$$$$x^3+z^3=3x+3y+4$$