[急,x^2-3x-1=0,求代数式1/x^2-2x-1的值.如果可能的话,可以让我更明白.

∵x^2-3x-1=0
∴ （x-3/2)²-9/4 -1=0
x=(3±√13)/2
当x=(3+√13)/2时
1/x^2-2x-1=1/(x-1)²-2=1/[(3+√13-2)/2]²-2=1/(14+2√13)/4 -2
=2/(7+√13-4)=2(3-√13)/(3+√13)(3-√13)=(√13-3)/2
当x=(3-√13)/2时
1/x^2-2x-1=1/(x-1)²-2=1/[(3-√13-2)/2]²-2=1/(14-2√13)/4 -2
=2/(7-√13-4)=2(3+√13)/(3+√13)(3-√13)=(-√13-3)/2

∵x²-3x-1=0
∴x-3-1/x=0
x-1/x=3
∵x²-2x-1
=x-2-1/x
=x-1/x-2
=3-2
=1
∴1/(x²-2x-1)=1/1=1