x^4-2x^3+2x-1=0 因式分解

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x^4-2x^3+2x-1=0 因式分解
x^4-2x^3+2x-1=0 因式分解

x^4-2x^3+2x-1=0 因式分解
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

x^4-2x^3+x^2-x^2+2x-1
=x^2(x^2-2x+1)-(x^2-2x+1)
=(x^2-1)(x+1)^2
=(X+1)(X-1)(x+1)^2
=(x+1)^3(x-1)