若a²-5a-1=0,求(a-2)分之(a-2)的立方-(a-1)²+1的值

题目

若a²-5a-1=0,求(a-2)分之(a-2)的立方-(a-1)²+1的值

答案

[(a-2)³-(a-1)²+1]/(a-2)
=[(a-2)³-a²+2a-1+1]/(a-2)
=[(a-2)³-a(a-2)]/(a-2)
=(a-2)²-a
=a²-4a+4-a
=a²-5a-1+5
=5