Question

若X=[根号（n+1）-根号n]除于[根号（n+1）+根号n],

Answer 1

x=[(n+1)-2根号n(n+1)+n]/(n+1-n)=2n+1-2根号n(n+1)

y=2n+1+2根号n(n+1)

x+y=4n+2 xy=1

∵x^2+1519xy+y^2=2001

即(x+y)2+1517xy=2001

∴16n^2+16n+4+1517=2001

16n^2+16n-480=0

n^2+n-30=0

∴n=5(-6舍去）