回復 3# leo790124 的帖子
\(\begin{array}{l}
{x^{15}} - 1\\
= \left( {{x^5} - 1} \right)\left( {{x^{10}} + {x^5} + 1} \right)\\
= \left( {x - 1} \right)\left( {{x^4} + {x^3} + {x^2} + x + 1} \right)\left( {{x^2} + x + 1} \right)\left( {{x^8} - {x^7} + {x^5} - {x^4} + {x^3} - x + 1} \right)
\end{array}\)
易知\(\cos \frac{2\pi }{15}+i\sin \frac{2\pi }{15}\)是\({{x}^{8}}-{{x}^{7}}+{{x}^{5}}-{{x}^{4}}+{{x}^{3}}-x+1=0\)之根
