Question

若x+y=1,xy=-1,求x^3+y^3的值 请写明过程、、

点解x^3+y^3=(x+y)(x^2-xy+y^2)？

Answer 1

x³+y³
=(x+y)(x²-xy+y²)
=(x+y)[(x+y)²-3xy]
=1*[1+3]
=4

x^3+y^3=(x+y)(x^2-xy+y^2)
这个是立方和公式，大概你没学~

推导：
x³+y³=(x+y)(x²+y²)-xy(x+y)=(x+y)(x²-xy+y²)

Answer 2

x^3+y^3
=(x+y)(x^2-xy+y^2)
=(x+y)(x^2-xy+y^2+2xy-2xy)
=(x+y)[(x+y)^2-3xy]
x+y=1 xy=-1 代入
得 1*[(1)^2-3*(-1)]
=1+3=4

Answer 3

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

x^3+y^3=X^3+X^2Y+Y^3-X^2Y=YO 用因式分解可以推出