已知x+y=3,x²+y²-3xy=4.求x³y+xy³的值

已知x+y=3,x²+y²-3xy=4.求x³y+xy³的值
已知x+y=3,x²+y²-3xy=4.求x³y+xy³的值

已知x+y=3,x²+y²-3xy=4.求x³y+xy³的值
x+y=3; (x+y)²=x²+y²+2xy=9;
x²+y²=9-2xy=4+3xy;
xy=1; x²+y²=7
x³y+xy³=xy(x²+y²)=1×7=7