x^4-2x^3-x^2+2x+1
=(x^4-2x^3+x^2)-2x^2+2x+1
=x^2(x-1)^2-2x(x-1)+1
=[x(x-1)-1]^2
=(x^2-x-1)^2
故x^4-2x^3-x^2+2x+1=0
(x^2-x-1)^2=0
x^2-x-1=0
x=(1±√5)/2