Question

若实数x，y满足xy+x+y+7=0，3x+3y=9+2xy，则x 2 y+xy 2 =______

若实数x，y满足xy+x+y+7=0，3x+3y=9+2xy，则x 2 y+xy 2 =______．

Answer 1

∵ 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 ∴x 2 y+xy 2 =xy（x+y）=-6×（-1）=6 故答案为6