解 由题意可得 m+n=3 mn=1
2m^2+4n^2-6n+1999=2m^2+4n^2-2n(m+n)+1999=2m^2+2n^2-2mn+1999
=2(m+n)^2--6mn+1999
=2*3*3-6*1+1999
=2011