若a^3-3a+1=0,则(a^3)/(a^6+1 - 知识问答

若a^3-3a+1=0,则(a^3)/(a^6+1)的值为

1个回答

两边同时除以a,得
a-3+1/a=0
a+1/a=3
先求
(a^6+1)/a^3
=a^3+1/a^3
=(a+1/a)(a^2-1+1/a^2)
=3×[(a+1/a)^2-3]
=3×(3^2-3)
=3×6
=18
所以a^3/（a^6+1）=1/18.

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