∵a.b是方程x²-2√3x+2=0的两根∴a+b=2√3; ab=2∵2sin（A+B）=√3∴sinC=sin(A+B)=√3/2∵锐角三角形∴C=60°∴cosC=1/2∴AB²=BC²+AC²-2*BC*AC*cosC=a²+b²-2ab*1/2=a²+b²-ab=(a+b)²-3ab=(2√3)²-3*2=12-6=6∴AB=√6
