Question

已知xy=-2,x-y=3求(x+y)(x-y)-y^2-(6x^2y-2xy^2)/2y的值。

Answer 1

(x+y)(x-y)-y²-(6x²y-2xy²)/2y
=x²-y²-y²-3x²+xy
=-2y²-2x²+xy
=-2(x²+y²)+xy
由于xy=-2,x-y=3，所以x²+y²=(x-y)²+2xy=9-4=5
将xy=-2，x²+y²=5代入上式得到：
(x+y)(x-y)-y²-(6x²y-2xy²)/2y
=-2(x²+y²)+xy
=-2*5-2
=-12

Answer 2

由xy=-2,x-y=3可得：x=1,y=-2或x=2,y=-1
当x=1,y=-2时，(x+y)(x-y)-y^2-(6x^2y-2xy^2)/2y=-1*3-4-（-12-8）/（-4）=-6
当x=2,y=-1时，(x+y)(x-y)-y^2-(6x^2y-2xy^2)/2y=3-1-（-24-4）/（-2）=-12

Answer 3

因为xy=-2,x-y=3
所以x=1,y=-2或x=2,y=-1（代入法）
当x=1,y=-2时，(x+y)(x-y)-y^2-(6x^2y-2xy^2)/2y=-1*3-4-（-12-8）/（-4）=-6
当x=2,y=-1时，(x+y)(x-y)-y^2-(6x^2y-2xy^2)/2y=3-1-（-24-4）/（-2）=-12