Question

x+y=1,x²+Y²=3。求X³+Y³=?

Answer 1

X³+Y³=(x+y)(x²+Y²-xy)
2xy==(x+y)²-(x²+Y²)
xy=-1
X³+Y³=(x+y)(x²+Y²-xy)=1*(3+1)=4

Answer 2

2XY=(X+Y)²-(X²+Y²)=1²-3=-2，所以XY=-1
X³+Y³
=(X+Y)(X²-XY+Y²)
=1×(3+1)
=4