f(x)=1/2+1/2cos2x+√3/2sin2x-1/2=√3/2sin2x+1/2cos2x=sin(2x+π/6)x在[0,π/2]2x+π/3在[π/6，7π/6]2x+π/6＝π/2时有最大值x=π/6 ,最大值=12)f(A/2)=sin(A/2+π/6)=1A/2+π/6=π/2A=2π/3a^2=b^2+c^2-2bccos2π/3=1+16-8*1/2=13a=√13
