x^2+xy+y^2-3x-3y+3=0x^2+(y-3)x+y^2-3y+3=0△=(y-3)^2-4(y^2-3y+3)=y^2-6y+9-4y^2+12y-12=-3y^2+6y-3=-3(y-1)^2≤0由于有实数根,判别式必须≥0故-3(y-1)^2=0y=1,带入,得x^2-2x+1=0(x-1)^2=0x=1.综上所述,实数根为x=...