已知a^2-5a-1=0 a^3-4a^2-6a-100

题目

已知a^2-5a-1=0 a^3-4a^2-6a-100

答案

a²=5a+1
a²用5a+1代替
则a³=a×a²
=a(5a+1)
=5a²+a
=5(5a+1)+a
=26a+5
原式=(26a+5)-4(5a+1)-6a-100
=26a+5-20a-4-6a-100
=-99