x+y=1 xy=-1 求x3+y3=?如题,我急需啊~~~希望快点,在线等

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x+y=1  xy=-1   求x3+y3=?如题,我急需啊~~~希望快点,在线等
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x+y=1 xy=-1 求x3+y3=?如题,我急需啊~~~希望快点,在线等
x+y=1 xy=-1 求x3+y3=?
如题,我急需啊~~~希望快点,在线等

x+y=1 xy=-1 求x3+y3=?如题,我急需啊~~~希望快点,在线等
x+y=1,
(x+y)^2=1,x^2+2xy+y^2=1,
x^2+y^2=3
x^3+y^3
=(x+y)(x^2-xy+y^2)
=4

根据前面两个条件可以求出(x+y)^3,开根号可以得到(x+y)的值

(X³+Y³)=(X+Y)(X²-XY+Y²)
(X+Y)=1
X²+2XY+Y²=1 (减三次XY=-1)
X²-XY+Y²=1+3=4
(X³+Y³)=(X+Y)(X²-XY+Y²)=1*4=4

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