Question

If $x+y+z=0$, what can be said about $x^3+y^3+z^3$?

• A. $x^3+y^3+z^3=0$
• B. $x^3+y^3+z^3=3$
• C. $x^3+y^3+z^3=3xyz$
• D. $x^3+y^3+z^3=x^{2}y+y^{2}z+z^{2}x$

Answer 1

The correct option is C $x^3+y^3+z^3=3xyz$

We know,

$x^3+y^3+z^3-3xyz$ = $(x+y+z)$ ($x^2+y^2+z^2-xy-yz-zx$)

$\because$ $x+y+z=0$

We have,
$x^3+y^3+z^3-3xyz=0$

$\Rightarrow$
$x^3+y^3+z^3=3xyz$