Question

设x=根号n+1-根号n/根号n+1+根号n y=根号n+1+根号n/根号n+1-根号n n为自然数若

Answer 1

设x=根号n+1-根号n/根号n+1+根号n =(根号n+1-根号n)^2

y=根号n+1+根号n/根号n+1-根号n =(根号n+1+根号n)^2

所以x+y=2(n+1)+2n=4n+2=2(2n+1)

xy=1

2x^+217xy+2y^

=2(x+y)^2+213xy

=8(2n+1)^2+213

=2013

(2n+1)^2=1800/8=225

2n+1=15

n=7