Question

Let $x+y+z=0$ then the value of $x^3+y^3+z^3=?$

Answer 1

Given,

$x+y+z=0$

or, $x+y=-z$ ……..$\left(1\right)$

cubing both sides we get,

$(x+y{)}^3=-z^3$

or, $x^3+y^3+3xy(x+y)=-z^3$

or, $x^3+y^3-3xyz=-z^3$ [using $\left(1\right)$]

or, $x^3+y^3+z^3=3xyz$.