已知xy+x-y+1=6,(1-x^2)(1-y^2)+4xy=48,求xy-x+y+1的值
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已知xy+x-y+1=6,(1-x^2)(1-y^2)+4xy=48,求xy-x+y+1的值
![已知xy+x-y+1=6,(1-x^2)(1-y^2)+4xy=48,求xy-x+y+1的值](/uploads/image/z/16692876-36-6.jpg?t=%E5%B7%B2%E7%9F%A5xy%2Bx-y%2B1%3D6%2C%281-x%5E2%29%281-y%5E2%29%2B4xy%3D48%2C%E6%B1%82xy-x%2By%2B1%E7%9A%84%E5%80%BC)
(1-x^2)(1-y^2)+4xy=48
1-x²-y²+x²y²+4xy=48
(x²y²+2xy+1)-(x²-2xy+y²)=48
(xy+1)²-(x-y)²=48
(xy+x-y+1)(xy-x+y+1)=48
xy+x-y+1=6
所以xy-x+y+1=8
1-x²-y²+x²y²+4xy=48
(x²y²+2xy+1)-(x²-2xy+y²)=48
(xy+1)²-(x-y)²=48
(xy+x-y+1)(xy-x+y+1)=48
xy+x-y+1=6
所以xy-x+y+1=8
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