Question

If $x+y+z=0$, show that $x^2+y^3+z^3=3xyz$.

Answer 1

Given,

$x+y+z=0$
or, $x+y=-z$......(1).

Now cubing both sides we get,

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

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

or, $x^3+y^3+z^3=3xyz$. [ Using (1)]