已知x+y=3,x²+y²-3xy=4,求下列格式的值(1)xy(2)x³y+xy³
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![已知x+y=3,x²+y²-3xy=4,求下列格式的值(1)xy(2)x³y+xy³](/uploads/image/z/4351556-20-6.jpg?t=%E5%B7%B2%E7%9F%A5x%2By%3D3%2Cx%26%23178%3B%2By%26%23178%3B-3xy%3D4%2C%E6%B1%82%E4%B8%8B%E5%88%97%E6%A0%BC%E5%BC%8F%E7%9A%84%E5%80%BC%281%29xy%282%29x%26%23179%3By%2Bxy%26%23179%3B)
已知x+y=3,x²+y²-3xy=4,求下列格式的值(1)xy(2)x³y+xy³
已知x+y=3,x²+y²-3xy=4,求下列格式的值
(1)xy
(2)x³y+xy³
已知x+y=3,x²+y²-3xy=4,求下列格式的值(1)xy(2)x³y+xy³
1)∵x+y=3
∴(x+y)²=9
即x²+2xy+y²=9
而x²+y²-3xy=4
∴2xy-(-3xy)=9-4
即5xy=5
∴xy=1
(2)∵(x+y)²=x²+2xy+y²=9
∴x²+y²=9-2xy=7
∴x³y+xy³=xy(x²+y²)
=1×7
=7
x+y=3,x²+y²-3xy=4,
(x+y)²=x²+2xy+y²=x²-3xy+y²+5xy=9
4+5xy=9
得 xy=1
x²+y²=(x+y)²-2xy=9-2=7
x³y+xy³=xy(x²+y²)=x²+y²=7
①x+y=3 ②x²+y²-3xy=4
①²-②得5xy=5,xy=1
原式=xy(x²+y²)=4+3xy=7
x2+y2-3xy=(x+y)2-5xy=4可得xy=1
x3y+xy3=xy(x2+y2)=xy((x+y)2-2xy)=7