Question

If $x+y+z=0$, then $x^2+y^3+z^3=$

• A. $xyz$
• B. $2xyz$
• C. $3xyz$
• D. None

Answer 1

The correct option is C $3xyz$

Given $x+y+z=0$, then $x^3+y^3+z^3=3xyz$

We know that identities is $x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)$

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

$\Rightarrow x^3+y^3+z^3-3xyz=\left(0\right)(x^2+y^2+z^2-xy-yz-zx)$

$\Rightarrow x^3+y^3+z^3-3xyz=0$

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