m^2+n^2-mn+3m-2n+7
=m^2-(n-3)m+n^2-2n+7
=[m-(n-3)/2]^2-(n-3)^2/4+n^2-2n+7
=[m-(n-3)/2]^2+3n^2/4-n/2+19/4
=[m-(n-3)/2]^2+3/4(n-1/3)^2+14/3
>=14/3
所以最小值是14/3,当 n=1/3,m=-4/3时取等