<s>[INST] Find the solution set of $x+y+z=0, xy+yz+zx=0,x^3+y^3+z^3=-3$ Find the solution set of the equations
$x+y+z=0$
$xy+yz+zx=0$
$x^3+y^3+z^3=-3$

Since $x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)$
Put $x+y+z=0$ and $xy+yz+zx=0$ and $x^3+y^3+z^3=-3$,we get
$-3-3xyz=0$
$xyz=-1$
But i dont know how to proceed from here?Please help me.Thanks.
 [/INST] use Vieta theorem ,then $x,y,z$ is 
$$t^3+1=0$$three roots
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