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

题目

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
若2x^+217xy+2y^=2013求n的值

答案

设x=根号n+1-根号n/根号n+1+根号n =(根号n+1-根号n)^2y=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=12x^+217xy+2y^=2(x+y)^2+213xy=8(2n+1)^2+213=2013(2n+1)^2=1800/8=2252n...