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