1 已知1/n - 1/m - 1/(n+m)=0 则（m/n + n/m）²=

题目

1 已知1/n - 1/m - 1/(n+m)=0 则（m/n + n/m）²=
2 已知X²-3y²=2xy x＞0 y＞0 则(x+2y)/(x-y)的值是

答案

1/n - 1/m - 1/(n+m)=0
(m-n)/mn=1/(m+n)
m^2-n^2=mn
两边同除mn,得
m/n-n/m=1
（m/n + n/m）^2=(m/n-n/m)^2+4=1+4=5
(x+2y)/(x-y)
=(x+2y)(x+y)/(x-y)(x+y)
=(x^2+3xy+2y^2)/(x^2-y^2)
=(3y^2+2xy+3xy+2y^2)/(3y^2+2xy-y^2)
=5(y^2+xy)/2(y^2+xy)
=5/2