>566
a^2=b^2+c^2-2bc*cosA
c=(2cosA+1)b
a/sinA=c/sinC
a=2√3*sinA/3*c=2√3*sinA(2cosA+1)/3*b
a^2=b^2+bcに代入
(2√3*sinA(2cosA+1)/3*b)^2=b^2+(2cosA+1)b^2
cosA=pとする
8p^4+8p^3-6p^2-5p+1=0
(p+1)(8p^3-6p+1)=0