14/03/11 08:44:37.02
間違えた
a=cos(2π/7),b=cos(4π/7),c=cos(8π/7),α=a^(1/3),β=b^(1/3),γ=c^(1/3),
s=α+β+γ,t=αβ+βγ+γα,x=s^3とおく
a+b+c=-1/2,ab+bc+ca=-1/2,abc=1/8
↓
s(ss-3t)=-2,2t(2tt-3s)=-5
↓
4xxx-30xx+75x+32=0
s=x^(1/3)=[5/2-3/2*7^(1/3)]^(1/3)
14/03/11 08:44:37.02
間違えた
a=cos(2π/7),b=cos(4π/7),c=cos(8π/7),α=a^(1/3),β=b^(1/3),γ=c^(1/3),
s=α+β+γ,t=αβ+βγ+γα,x=s^3とおく
a+b+c=-1/2,ab+bc+ca=-1/2,abc=1/8
↓
s(ss-3t)=-2,2t(2tt-3s)=-5
↓
4xxx-30xx+75x+32=0
s=x^(1/3)=[5/2-3/2*7^(1/3)]^(1/3)