Question

已知a加a分之一等于二,求a的四次方加a的平方加一分之a方的值

Answer 1

a+1/a=2 (a+1/a)^2=4 a^2+2+1/a^2=4 a^2+1/a^2=2

a^2/(a^4+a^2+1)

=a^2/[a^2(a^2+1+1/a^2)]

=1/(a^2+1/a^2+1)]

=1/(2+1)

=1/3