Question

已知x+y=3，x²+y²-2xy=4，则x³y+xy³的值为

Answer 1

x³y+xy³=xy(x^2+y^2)
x+y=3，平方：x^2+y^2 +2xy=9 ----(1)
x²+y²-2xy=4 ----(2)
(1) -(2)得：xy=5/4
(1)+(2)得：x^2+y^2= 13/2
x³y+xy³=xy(x^2+y^2)= 65/8

Answer 2

x+y=3，平方：x^2+y^2 +2xy=9 ----(1)
x²+y²-2xy=4 ----(2)
(1) -(2)得：xy=5/4
(1)+(2)得：x^2+y^2= 13/2
x³y+xy³=xy(x^2+y^2)= 65/8

Answer 3

解：x＋y＝3
﹙x＋y﹚²＝3²
x²＋y²＋2xy＝9…………①
x²＋y²－2xy＝4…………②
①＋②得：x²＋y²＝13/2

①－②得：xy＝5/2
∴x³y＋xy³＝xy﹙x²＋y²﹚
＝5/2×13/2
＝65/4
∴

Answer 4

x^2+y^2 +2xy=9
x²+y²-2xy=4
解得
(xy=5/4
x^2+y^2= 13/2
x³y+xy³=xy(x^2+y^2)= 65/8

Answer 5

5 x=1/2 y=5/2 或 x=5/2 y=1/2 代入答案都一样