代數方程 ( x ) π 6 = ( x − 1 ) 2 π 3 {\displaystyle {{\bigg (}x{\bigg )}}^{\frac {\pi }{6}}={{\bigg (}x-1{\bigg )}}^{\frac {2\pi }{3}}}
之根為 x = 12 + ( 36 ) 1 3 ( 18 + 2 849 ) 1 3 − 8 ( 3 9 + 849 ) 1 3 12 + {\displaystyle 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}}+}
( 36 ) 1 3 8 ( 3 9 + 849 ) 1 3 − ( 18 + 2 849 ) 1 3 + 12 ( 18 + 2 849 ) 1 3 − 8 ( 3 9 + 849 ) 1 3 12 {\displaystyle {\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}}}
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