(In reply to
computer solution (spoiler) by Charlie)
The behavior you noted happens because the two solutions are two of the three complex cube roots of one.
x=cos(120)+i*sin(120) and x=cos(240)+i*sin(240).
So if you square either of them you get the other, but cubing gives 1.

Posted by Jer
on 20150114 11:26:08 