已知xy=1,y=1/(2-√3),则1/(x+1)+1/(y+1)

y=1/(2-√3)=2+√3

xy=1,则x=1/y,x=2-√3

所以x+y=4

1/(X+1)+1/(Y+1)=(x+y+2)/(xy+x+y+1)

然后代入:答案为1

y=1/(2-√3)=(2+根号3)/[(2-根号3)(2+根号3)=2+根号3,

xy=1,则x=1/y=2-根号3

1/(X+1)+1/(Y+1)=1/(3-根号3)+1/(3+根号3)

=[3+根号3+3-根号3]/(3-根号3)(3+根号3)

=6/(9-3)

=1

1/（x+1)+1/(y+1)=(x+y+2)/(x+y+xy+1) 因为xy=1 故=(x+y+2)/(x+y+2)=1

xy=1,y=1/(2-√3)
那么
x＝2-√3

1/(x+1)+1/(y+1)
＝1/(2-√3+1)+1/[1/(2-√3)+1]
＝1/(3-√3)+(2-√3)/(3-√3)
＝(3-√3)/(3-√3)
＝1