For real numbers $a$, $b$, $c$ and $d$ holds: $$ a+b+c+d=0$$$$a^3+b^3+c^3+d^3=0$$Prove that sum of some two numbers $a$, $b$, $c$ and $d$ is equal to zero
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2010
Tags: algebra, Bosnia
For real numbers $a$, $b$, $c$ and $d$ holds: $$ a+b+c+d=0$$$$a^3+b^3+c^3+d^3=0$$Prove that sum of some two numbers $a$, $b$, $c$ and $d$ is equal to zero