Question

x1 x2是方程2x的平方-3x-1=0的两个根

Answer 1

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=3/2 x1x2=-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