已知x^2-4x+1=0;
x^2=4x-1
(1)x^4-2x^3-8x^2+6x+2012
=x^4-4x^3+x^2+2x^3-9x^2+6x+2012
=x^2(x^2-4x+1)+2(x^3-4x^2+x)-x^2+4x+2012
=x^2(x^2-4x+1)+2x(x^2-4x+1)-(x^2-4x+1)+1+2012
=2013
(2)5x^2-12x+2/x^2
=((3x^2-12x+3)+2x^2-1)/x^2
=(3(x^2-4x+1)+2x^2-1)/x^2
=(2x^2-1)/x^2
=2-1/x^2
x^2-4x+1=0
x=4+√16-4/2=2+√3
或x=4-√16-4/2=2-√3
当x=2+√3
则上式==2-1/x^2
=2-1/(2+√3)^2
=2-(2-√3)^2/(2+√3)^2(2-√3)^2
=2-(4-2√3+3)/(4-3)^2
=2√3-5
当x=2-√3
则上式==2-1/x^2
=2-1/(2-√3)^2
=2-(2+√3)^2/(2+√3)^2(2-√3)^2
=2-(4+2√3+3)/(4-3)^2
=-2√3-5