∵x²-3x-1=0
∴x²-3x=1
∴x²=3x+1
∴x³=3x²+x
=3(3x+1)+x
=10x+3
∴2x³-3x²-11x+8
=2(10x+3)-3(3x+1)-11x+8
=20x+6-9x-3-11x+8
=11