Question

已知实数m,n满足1/(m+n)+1/（m-n）=n/(m^2-n^2),求2mn+n^2/m^2

Answer 1

1（m-n）/(m+n)(m-n)+1(m+n)/(m-n)(m+n)
=(m-n)/(m^2-n^2)+(m+n)/(m^2-n^2)
=2m/(m^2-n^2)
=n/(m^2-n^2)
得2m=n
故，2mn+n^2/m^2=4+n^2=4+4m^2

难道你的题目是求（2mn+n^2）/m^2？？？？？？？？？？？？？？

追问

是的

追答

哦，同理，把2m=n代入，
（2mn+n^2）/m^2=(4m^2+4m^2)/m^2=8

Answer 2

1/(m+n)+1/（m-n）=n/(m^2-n^2)
两边同乘m^2-n^2
m-n+m+n=n(m≠n)
n=2m
(2mn+n^2)/m^2=(4(m^2)+4(m^2))/m^2=8

Answer 3

1/(m+n)+1/(m-n)=(m-n+m+n)/(m^2-n^2)=2m/(m^2-n^2)
由题知，则2m=n,
2mn+n^2/m^2=4(m^2+1)或（4+n^2)