解决个数学题

-1/12

x+1/x=3 --> x^2=1-3x

x^2/(x^4+x^2+1)=(1-3x)/[(1-3x)^2+1-3x-1]
=(1/3)(1-3x)/(3x^2-3x+1)
=(1/3)(3x-1)/(-12x+4)
=-1/12

x+1/x=3
方程两边同时乘以X
x+1=3x
解得x=0.5
把x=0.5代入得
0.5^2/0.5^4+0.5^2+1
=4+0.25+1
=5.25

可以解得 x=1/2
代入求得x^2/x^4+x^2+1=4+1/4+1=21/4

x+1/x=3
(x+1/x)^2=9
x^2+2x*(1/x)+1/x^2=9
x^2+2+1/x^2=9
x^2+1+1/x^2=8
(x^4+x^2+1)/x^2=8
x^2/(x^4+x^2+1)=1/8