已知a²-3a+1=0,则a³÷﹙a³+1﹚的值为

题目

已知a²-3a+1=0,则a³÷﹙a³+1﹚的值为

答案

a2-3a+1=0
显然a=0不能满足要求,因此两边都除以a,
=>
a+1/a-3=0
=>a+1/a=3
a^2+1/a^2=(a+1/a)^2-2=3^2-2=7
a^3+1/a^3
=(a+1/a)(a^2+1/a^2-1)
=3*(7-1)
=18所以 a³÷﹙a³+1﹚=1/18