若已知a2-3a+1=0 求:a4+1/a4的值?

若已知a2-3a+1=0 求:a4+1/a4的值?
若已知a2-3a+1=0 求:a4+1/a4的值?

若已知a2-3a+1=0 求:a4+1/a4的值?
a^2-3a+1=0
a-3+1/a=0
a+1/a=3
a^4+1/a^4
=a^4+1/a^4+2-2
=(a^2+1/a^2)^2-2
=[(a+1/a)^2-2]^2-2
=[3^2-2]^2-2
=47