因式分解 X3-3X2+X+1=0

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因式分解 X3-3X2+X+1=0
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因式分解 X3-3X2+X+1=0
因式分解 X3-3X2+X+1=0

因式分解 X3-3X2+X+1=0
X3-3X2+X+1=0
x^3-x^2-2x^2+x+1=0
x^2(x-1)-(2x+1)(x-1)=0
(x-1)(x^2-2x-1)=0

X3-3X2+X+1=0
(x³-x²)-(2x²-2x)-(x-1)=0
x²(x-1)-2x(x-1)-(x-1)=0
(x-1)(x²-2x-1)=0
(x-1)(x²-2x+1-2)=0
(x-1)[(x-1)²-2]=0
(x-1)(x-1+根号2)(x-1-根号2)=0
x=1或x=1-根号2或x=1+根号2

X³-3X²+X+1=0
x(x²-2x+1)-x²+1=0
x(x-1)²-(x-1)(x+1)=0
(x-1)(x²-x-x-1)=0
(x-1)(x²-2x-1)=0

X³-3X²+X+1= (X³-3X²+3X-1)+(2-2x)=(x-1)³-(x-1)=(x-1)[(x²-2x)-1]=x(x-1)(x-2)