若x+1/x=3,则x²/x四次方x²+1的值为

问题描述:

若x+1/x=3,则x²/x四次方x²+1的值为

答:
x+1/x=3
x^2/(x^4+x^2+1)
=1/(x^2+1/x^2+1)
=1/[(x+1/x)^2-1]
=1/(3^2-1)
=1/8