a^2-3a+1=0,
二边同除以：a
a-3+1/a=0
(1)
a+1/a=3
(2)
a^2+1/a^2
=(a+1/a)^2-2
=3^2-2
=7
(3)
a^4+1/a^4
=(a^2+1/a^2)^2-2
=7^2-2
=49-2
=47