(b/a)^2+(2根号3/a)^2=1
sinθ=b/a,cosθ=2根号3/a
a=2根号3/cosθ,b=2根号3sinθ/cosθ
a^2+b^2+ab=12(1+sin^2θ+sinθ)/cos^2θ={12(sinθ+1/2)^2+9}/(1-sin^2θ)
sinθ=-1/2时,最小值=9/(1-1/4)=12