Question

已知x+y=3,x^2+y^2-3xy=4,则x^3y+xy^3的值为

Answer 1

解：由题耐销意可得：
x^2+y^2=(x+y)^2-2xy=9-2xy
所肆唤以裂亩凯x^2+y^2-3xy=9-5xy=4
所以xy=1
x^3y+xy^3=xy(x^2+y^2)=x^2+y^2=7

Answer 2

x^3y+xy^3＝(x^2+y^2)xy
由已知平方得：x^2+y^2+2xy=9①
x^2+y^2-3xy=4②
由①州租②，解得念迹备
x^2+y^2＝7
xy＝1
代入x^3y+xy^3＝仔毁(x^2+y^2)xy
，得x^3y+xy^3＝7

Answer 3

x+y=3,
x²+y²+2xy=9①
而x²+y²茄卖漏配模-3xy=4②颤烂
①-②得5xy=5,即xy=1
x²+y²=7
x^3y+xy^3
=xy(x²+y²)
=7