Question

已知a^2-4a+1=0，求a^2/a^4+a^2+1的值

Answer 1

a^2-4a+1=0
除以a得 a-4+1/a=0
a+1/a=4
(a^4+a^2+1)/a^2
=a²+1+1/a²
=(a+1/a)²-1
=4²-1
=15
∴a^2/﹙a^4+a^2+1﹚=1/15

Answer 2

15.
a^2=4a-1
a^2/a^4+a^2+1=1/a^2+a^2+1=(1+a^4+a^2)/a^2=((4a-1)^2+4a)/a^2=(16a^2-4a+1)/(4a-1)
=(16(4a-1)-(4a-1))/(4a-1)=16-1=15