X y is a real number and X & # 178; - 2x + √ XY-2 = - 1, find the value of 1 / XY + 1 / (x + 1) (y + 1) +. + 1 / (x + 2006) (y + 2006) Sorry for the inconvenience

X y is a real number and X & # 178; - 2x + √ XY-2 = - 1, find the value of 1 / XY + 1 / (x + 1) (y + 1) +. + 1 / (x + 2006) (y + 2006) Sorry for the inconvenience

(x-1)²+√(xy-2)=0
∴x-1=0
xy-2=0
∴x=1
y=2
1/xy+1/﹙x+1﹚﹙y+1﹚+.+1/﹙x+2006﹚﹙y+2006﹚
=1/1*2+1/2*3+1/3*4+…… +1/2007*2008
=1-1/2+1/2-1/3+1/3-…… -1/2007+1/2007-1/2008
=1-1/2008
=2007/2008