若X=[根号（n+1）-根号n]除于[根号（n+1）+根号n],（接上）y=[根号（n+1）+根号n]除于根号（n+1）+根号n],当n取何值时,x^2+1519Xy+y^2=2001提示:

Question

若X=[根号（n+1）-根号n]除于[根号（n+1）+根号n],
（接上）y=[根号（n+1）+根号n]除于根号（n+1）+根号n],当n取何值时,x^2+1519Xy+y^2=2001
提示:

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）