Question

a + b + c = 0, then prove that $a^3+b^3+c^3=3abc$

Answer 1

Given $a+b+c=0$

$⟹a+b=-c$

cubing on both sides

$(a+b{)}^3=-c^3$

$a^3+b^3+3ab(a+b)=-c^3$

$a^3+b^3+c^3+3ab(-c)=0$

$⟹a^3+b^3+c^3=3abc$