Question 78
Let $a,b$ be real numbers such that distinct real numbers $m,n,p$ satisfy
$$\begin{cases}m^3+am+b=0,\\n^3+an+b=0,\\p^3+ap+b=0.\end{cases}$$
Show that $m+n+p=0$.
$$\begin{cases}m^3+am+b=0,\\n^3+an+b=0,\\p^3+ap+b=0.\end{cases}$$
Show that $m+n+p=0$.