a^2-3a+1=0 则a^2+1/（a^2）= a^2

题目

a^2-3a+1=0 则a^2+1/（a^2）= a^2
a^2-3a+1=0 则a^2+1/（a^2）= a^2/（a^4+a^2+1）=

答案

a^2-3a+1=0,有
a^2+1=3a
两边除以a
a+1/a=3
两边平方
a^2+2+1/a^2=9
a^2+1/a^2=7
a^2/(a^4+a^2+1)
=1/(a^2+1+1/a^2)
=1/(7+1)
=1/8