已知xy+x-y+1=6,（1-x²）（1-y²）+4xy=48 求xy-x+y+1的值

已知xy+x-y+1=6,（1-x²）（1-y²）+4xy=48 求xy-x+y+1的值
已知xy+x-y+1=6,（1-x²）（1-y²）+4xy=48 求xy-x+y+1的值

已知xy+x-y+1=6,（1-x²）（1-y²）+4xy=48 求xy-x+y+1的值
xy+x-y+1=6
xy+1=6-(x-y)
(1-x²)(1-y²)+4xy=48
1-x²-y²+x²y²+4xy=48
x²y²+2xy+1-(x²-2xy+y²)=48
(xy+1)²-(x-y)²=48
[(x-y)-6]²-(x-y)²=48
x-y=-1
xy=6-(x-y)=7
xy-x+y+1=xy-(x-y)+1=7-(-1)+1=9