Question

若1/m+1/n=7/(m+n)，则n/m+m/n的值为？

Answer 1

1/m+1/n=7/(m+n)，
(m+n)^2=7mn
m^2+n^2=5mn
n/m+m/n=(m^2+n^2)/mn=5mn/mn=5
n/m+m/n=5

追问

(m+n)^2=7mn 这步怎么来的

追答

左边通分去分母

Answer 2

1/m+1/n=7/(m+n)
n/(mn)+m/(mn)=7/(m+n)
(n+m)/(mn)=7/(m+n)
(m+n)^2=7mn
(m+n)^2=7mn

n/m+m/n
=n^2/(mn)+m^2/(mn)
=(m^2+n^2)/(mn)
=(m^2+n^2+2mn-2mn)/(mn)
=(m^2+n^2+2mn)/(mn)-2mn/(mn)
=(m+n)^2/(mn)-2
=7mn/(mn)-2
=7-2
=5

Answer 3

1/m+1/n=7/(m+n)，
(m+n)/mn=7/(m+n)
∴(m+n)²=7mn
m²+n²=5mn

n/m+m/n=(m²+n²)/mn=5mn/mn=5