若x²-3x+1=0,则x²/x四次方+x²+1的值为___

若x²-3x+1=0,则x²/x四次方+x²+1的值为___
若x²-3x+1=0,则x²/x四次方+x²+1的值为___

若x²-3x+1=0,则x²/x四次方+x²+1的值为___
x²-3x+1=0
x^2+1=3x
x+1/x=3
(x+1/x)^2=9
x^2+1/x^2=7
x^2/(x^4+x^2+1)
=1/(x^2+1+1/x^2)
=1/(7+1)
=1/8

x²-3x+1=0
除以x得 x-3+1/x=0
x+1/x=3
(x^4+x²+1)/x²
=x²+1+1/x²
=(x+1/x)²-2+1
=3²-1
=8
∴x²/x四次方+x²+1=1/8

x^2-3x+1=0
x^2+1=3x (平方）
(x^2+1)^2=9x^2
x^4+2x^2+1=9x^2
x^4+x^2+1=8x^2
x^2/(x^4+x^2+1)=1/8