Question

已知x + y = -1, x y = -2,求代数式x3 - y3的值

Answer 1

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

x-2/x =-1
x^2+x-2=0
(x+2)(x-1)=0
x=1 or -2
case 1: when x=1 ,y= -2
x^3- y^3 = 1+8=9

when x=-2 ,y= 1
x^3-y^3 = -8 -1 =-9

ie x^3- y^3 = 9 or -9

Answer 2

x+y=-1
两边平方
x²+2xy+y²=1
所以x²+y²
=1-2xy
=5
所以原式=(x+y)(x²-xy+y²)
=-1*(5+2)
=-7