4x^2-4x+1+y^2+6y+9=0,(2x-1)^2+(y+3)^2=0.则2x-1=0,y+3=0,得x=1/2,y=-3,所以4x^2-12xy+9y^2=(2x-3y)^2=[2*(1/2)-3*(-3)]^2=100