若a+1\a=5,则a^2\a^4+a^2+1等于几

若a+1\a=5,则a^2\a^4+a^2+1等于几
若a+1\a=5,则a^2\a^4+a^2+1等于几

若a+1\a=5,则a^2\a^4+a^2+1等于几
a+1/a=5
a^2/(a^4+a^2+1)
=1/[a^2+1+(1/a^2)]
=1/[(a+1/a)^2-1]
=1/(5^2-1)
=1/24

先将a+1\a=5两边平方，带入后面为24