院系:李煌數學研究院/2018年暑假之研究

李煌定理

代数方程${{\bigg (}x{\bigg )}}^{\frac {\pi }{6}}={{\bigg (}x-1{\bigg )}}^{\frac {2\pi }{3}}$

之根为 $x={\frac {12+{{\bigg (}36{\bigg )}}^{\frac {1}{3}}{\sqrt {{\bigg (}18+2{\sqrt {849}}{\bigg )}^{\frac {1}{3}}-8{\bigg (}{\frac {3}{9+{\sqrt {849}}}}{\bigg )}^{\frac {1}{3}}}}}{12}}+$

${\frac {{{\bigg (}36{\bigg )}}^{\frac {1}{3}}{\sqrt {8{\bigg (}{\frac {3}{9+{\sqrt {849}}}}{\bigg )}^{\frac {1}{3}}-{\bigg (}18+2{\sqrt {849}}{\bigg )}^{\frac {1}{3}}+{\frac {12}{\sqrt {{\bigg (}18+2{\sqrt {849}}{\bigg )}^{\frac {1}{3}}-8{\bigg (}{\frac {3}{9+{\sqrt {849}}}}{\bigg )}^{\frac {1}{3}}}}}}}}{12}}$

参考

• 《南昌理工學院學報》.李煌

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