已知:a2-3a+1=0求a^3-2a^2-5a+1/(a^2+1)

题目

已知:a2-3a+1=0求a^3-2a^2-5a+1/(a^2+1)

答案

a^2-3a+1=0
移项得a^2=3a-1
(a^3-2a^2-5a+1)/(a^2+1)
=[a^2(a-2)-5a+1]/(3a-1+1)
=[(3a-1)(a-2)-5a+1]/(3a)
=(3a^2-6a-a+2-5a+1)/(3a)
=(3a^2-12a+3)/(3a)
=(a^2-4a+1)/(a)
=(3a-1-4a+1)/a
=-a/a
=-1