Question

已知1/m+1/n=1/m+n,则m*m/n*n+n*n/m*m

Answer 1

1/m+1/n=1/m+n

(m+n)/mn=1/(m+n)

mn=(m+n)^2

m^2n^2=(m+n)^4

m*m/n*n+n*n/m*m

=m^2/n^2+n^2/m^2

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

=[(m^2+n^2)^2-2m^2n^2]/(m^2n^2)

=(m^2+n^2)^2/(m^2n^2)-2

=[(m+n)^4+4m^2n^2-4mn(m+n)^2]/(m^2n^2)-2

=1+4-4-2

=-1