x1,x2是方程2x²-3x-1=0的根,则x1满足方程2x1²-3x1-1=0
另由韦达定理,得
x1+x2=3/2x1x2=-1/2
N=3x1²+x2²-3x1=2x1²-3x1-1+x1²+x2²+1
=0+(x1+x2)²-2x1x2+1
=(3/2)²-2(-1/2)+1
=9/4+1+1
=17/4