若x+y=1,x²+y²=3,求x^3+y^3

若x+y=1,x²+y²=3,求x^3+y^3
若x+y=1,x²+y²=3,求x^3+y^3

若x+y=1,x²+y²=3,求x^3+y^3
因为(x+y)=1
所以(x+y)^2=x^2+2xy+y^2=1
因为x^2+y^2=3
所以2xy=1-3=-2 xy=-1
(x+y)(x^2+y^2)=x^3+y^3+xy^2+yx^2=x^3+y^3+xy(y+x)=1*3=3
xy(x+y)=-1*1=-1
所以
x^3+y^3=3-(-1)=4
如果学过立方和公式就更好了.
更简单了就

2xy
=(x+y)^2-(x^2+y^2)
=1-3
=-2
xy=-1

x^3+y^3
=(x+y)(x^2-xy+y^2)
=1*(3+1)
=4

不懂可追问，有帮助请采纳，谢谢！

x+y=1,
(x+y)^2=x^2+2xy+y^2=3+2xy=1,
xy=-1
x^3+y^3=(x+y)(x^2-xy+y^2)=1*(3-(-1))=4

（x+y）^2=x^2+2xy+y^2=1，x^2+y^2=3，xy=-1
（x+y）^3=X^3+3X^2Y+3XY^2+Y^3=1，x^3+y^3=4