已知m^2+n^2+mn+m-n+1=0,求1/m+1/n我只记得结果是0,忘记做法了,

Question

已知m^2+n^2+mn+m-n+1=0,求1/m+1/n
我只记得结果是0,忘记做法了,

Answer 1

m^2+n^2+mn+m-n+1=0
2m^2+2n^2+2mn+2m-2n+2=0
(m^2+2m+1)+(n^2-2n+1)+(m^2+2mn+n^2)=0
(m+1)^2+(n-1)^2+(m+n)^2=0
m+1=0
n-1=0
m+n=0
m=-1,n=1
1/m+1/n
=-1+1
=0