填充第5題
以\(\displaystyle a=2\cos \frac{2\pi }{7},b=2\cos \frac{4\pi }{7},c=2\cos \frac{6\pi }{7}\)為三根之方程式為\({{x}^{3}}+{{x}^{2}}-2x-1=0\)
參考
https://math.pro/db/viewthread.php?tid=1041&page=1#pid15215
\(\begin{align}
& a+\frac{1}{a}+b+\frac{1}{b}+c+\frac{1}{c} \\
& =a+b+c+\frac{ab+bc+ca}{abc} \\
& =-\frac{1}{2}+\frac{\frac{-2}{4}}{\frac{1}{8}} \\
& =-\frac{9}{2} \\
\end{align}\)