Question

If $x^3+y^3+z^3=3xyz$, then $x+y+z=?$

• A. $-1$
• B. $0$
• C. $1$
• D. None of the above

Answer 1

The correct option is B $0$

We know that:

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

Let us consider, $(x+y+z)=0$.

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

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

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

Then, if $x^3+y^3+z^3=3xyz$, then $(x+y+z)=0$.

Therefore, option $A$ is correct.