Question

已知a的平方-3a+1=0,求代数式a的立方除（a的6次方+1）的值

Answer 1

a^2-3a+1=0

a-3+1/a=0

a+1/a=3

(a+1/a)^3=a^3+3a+3/a+1/a^3=a^3+1/a^3+3(a+1/a)

a^3+1/a^3=(a+1/a)^3-3(a+1/a)=3^3-3*3=18

a^3/(a^6+1)

=1/(a^3+1/a^3)

=1/18