已知a是方程x²-3x 1=0的根,求代数式(a³-2a²-5a+1)/(a²+1)
因为a是方程x²-3x+1=0的根
所以a²+1=3a ,a²-3a=-1
(a³-2a²-5a+1）/(a²+1)
=(a³-3a²+a²-5a+1)/(a²+1)
=[a(a²-3a)+a²-5a+1]/(a²+1)
=(-a+a²-5a+1)/(a²+1)
=(a²+1-6a)/(a²+1)
=(3a-6a)/3a
=-3a/3a
=-1