[-InnoXenT-]

$x^6-1 = 0$
$(x^2+x+1)(x^2-x+1)=0$
$x^2(x+1+\frac{1}{x})(x-1+\frac{1}{x})=0$
$(x+\frac{1}{x})^2-1=0$
$x^2+\frac{1}{x^2}=-1$