问题
填空题
若实数x,y满足xy+x+y+7=0,3x+3y=9+2xy,则x2y+xy2=______.
答案
∵xy+x+y+7=0 ① 3x+3y=9+2xy ②
∴①×2+②得5(x+y)=-5,即x+y=-1 ③
③代入①解得xy=-6
∴x2y+xy2=xy(x+y)=-6×(-1)=6
故答案为6
若实数x,y满足xy+x+y+7=0,3x+3y=9+2xy,则x2y+xy2=______.
∵xy+x+y+7=0 ① 3x+3y=9+2xy ②
∴①×2+②得5(x+y)=-5,即x+y=-1 ③
③代入①解得xy=-6
∴x2y+xy2=xy(x+y)=-6×(-1)=6
故答案为6