2017/035) a,b ,c are three distint real numbers and there are real numbers x,y such that $a^3+ax+y=0$, $b^3+bx+y=0$, $c^3+cx +y = 0$. Show that $a+b+c=0$

Let us consider the equation $f(p) = p^3 + px + y = 0$
The above equation is cubic in p and has 3 roots.
From the given condition a,b,c are three roots so the sum of roots = -  coefficient of $p^2$
hence a + b+ c = 0
Proved