1/m+1/n=4/(m^2+n^2),求m+n的值

1/m+1/n=4/(m^2+n^2)(m+n)/(mn)=4/(m^2+n^2)m+n=4mn/(m^2+n^2)

1/m+1/n=4/(m²+n²)设m=kn，k≠01/m+1/n=1/(kn)+1/n=(1+k)/(kn)4/(m²+n²)=4/(k²n²+n²)=4/[n²(k²+1)](k+1)/(kn)=4/[n²(k²+1)]n=4k/[(k+1)(k²+1)]m+n=n(k+1)=4k/(k²+1)1】若k>0m+n=4/(k+1/k)≥4/2=2等号当且仅当k=1时成立。2】若k<0m+n=4/(k+1/k)≤4/(-2)=-2等号当且仅当k=-1时成立。∵4/(m²+n²)>0，∴1/m+1/n>0，∴k<-1或者k>0。∴m+m不是定值。m+n<-2或者m+n≥2。

1/m+1/n=4/(m²+n²)n/mn+m/mn=4/(m²+n²)(m+n)/mn=4/(m²+n²)m+n=4mn/(m²+n²)