设m>n>0,m^2+n^2=4mn,求m^2-n^2/mn.我做的步骤如下：原式=(m^2-n^2)4mn/mn(m^2+n^2)=4m^3n-4mn^3/m^3n+mn^3=-4m^3+4mn^3/m^3n+mn^3=-4不

Question

设m>n>0,m^2+n^2=4mn,求m^2-n^2/mn.
我做的步骤如下：原式=(m^2-n^2)4mn/mn(m^2+n^2)
=4m^3n-4mn^3/m^3n+mn^3
= - 4m^3+4mn^3/m^3n+mn^3
= -4
不知道哪里错了,请各位指教指教.

Answer 1

由m^2+n^2=4mn,
得：m/n+n/m=4
平方,得：(m/n)^2+(n/m)^2+2=16
故(m/n)^2+(n/m)^2-2=12
(m/n-n/m)^2=12
因为m>n>0,所以有m/n>1>n/m
因此上式开方得：m/n-n/m=2 √3
故(m^2-n^2)/(mn)=m/n-n/m=2 √3