已知x + y = -1,x y = -2,求代数式x3 - y3的值
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已知x+y=-1,xy=-2,求代数式x3-y3的值已知x+y=-1,xy=-2,求代数式x3-y3的值已知x+y=-1,xy=-2,求代数式x3-y3的值x+y=-1(1)xy=-2(2)x-2/x
已知x + y = -1,x y = -2,求代数式x3 - y3的值
已知x + y = -1,x y = -2,求代数式x3 - y3的值
已知x + y = -1,x y = -2,求代数式x3 - y3的值
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
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
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