∵m,n是一元二次方程x²－3x＋1＝0的两根
∴ m²-3m+1=0 n²-3n+1=0 m+n=3 mn=1
∴2m²＋4n²－6n＋2003
=2m²+4mn+2n²+2n²-6n+2-4mn+2001
=2(m+n)²+2(n²-3n+1)-4mn+2001
=2×3²+2×0-4×1+2001
=11-4+2001
=2008