$x^2-x+1=0$----->$x+\frac{1}{x}=1$
$(x+\frac{1}{x})^3=1$
$x^3+\frac{1}{x^3}=-2$
$$x^9+x^{-9}+x^6+x^{-6}+x^3+x^{-3}+1=(x^9+\frac{1}{x^9})+(x^6+\frac{1}{x^6})+(x^3+\frac{1}{x^3})+1$$ $$=(x^3+\frac{1}{x^3})^3-3(x^3+\frac{1}{x^3})+(x^3+\frac{1}{x^3})^2-2+(x^3+\frac{1}{x^3})+1$$ $$=(x^3+\frac{1}{x^3})^3+(x^3+\frac{1}{x^3})^2-2(x^3+\frac{1}{x^3})-1$$ $$=-1$$
เอ๊ะ ผมทำผิดตรงไหนอ่ะครับ
