x5+x4+1因式分解

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x5+x4+1因式分解x5+x4+1因式分解x5+x4+1因式分解x^5+x^4+1=x^3(x^2+x+1)-(x^3-1)=x^3(x^2+x+1)-(x-1)(x^2+x+1)=(x^3-x+1

x5+x4+1因式分解
x5+x4+1因式分解

x5+x4+1因式分解
x^5+x^4+1
=x^3(x^2+x+1)-(x^3-1)
=x^3(x^2+x+1)-(x-1)(x^2+x+1)
=(x^3-x+1)(x^2+x+1)

x^5+x^4+1
=x^3(x^2+x+1)-(x^3-1)
=x^3(x^2+x+1)-(x-1)(x^2+x+1)
=(x^3-x+1)(x^2+x+1)

x5+x4+1
=x^3(x^2+x+1)-(x^3-1)
=x^3(x^2+x+1)-(x-1)(x^2+x+1)
=(x^3-x+1)(x^2+x+1)
其中x^3-x+1还可以进行分解,分解成(x-a)(x^2-bx+c)
其中a=-1/6*(108+12*69^(1/2))^(1/3)-2/(108+12*69^(1/2))^(1/3)
x5...

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x5+x4+1
=x^3(x^2+x+1)-(x^3-1)
=x^3(x^2+x+1)-(x-1)(x^2+x+1)
=(x^3-x+1)(x^2+x+1)
其中x^3-x+1还可以进行分解,分解成(x-a)(x^2-bx+c)
其中a=-1/6*(108+12*69^(1/2))^(1/3)-2/(108+12*69^(1/2))^(1/3)
x5+x4+1=0的所有根为:
x1=-1/2+1/2*i*3^(1/2)
x2=-1/2-1/2*i*3^(1/2)
x3=-1/6*(108+12*69^(1/2))^(1/3)-2/(108+12*69^(1/2))^(1/3)
x4=1/12*(108+12*69^(1/2))^(1/3)+1/(108+12*69^(1/2))^(1/3)+1/2*i*3^(1/2)*(-1/6*(108+12*69^(1/2))^(1/3)+2/(108+12*69^(1/2))^(1/3))
x5=1/12*(108+12*69^(1/2))^(1/3)+1/(108+12*69^(1/2))^(1/3)-1/2*i*3^(1/2)*(-1/6*(108+12*69^(1/2))^(1/3)+2/(108+12*69^(1/2))^(1/3))
其中i=(-1)的平方,表示虚数
上面所有根中,x1,x2和x4,x5都是对偶的根,x1,x2形成了因式(x^2+x+1)
x4,x5形成了因式(x^2-bx+c),x3=a
如果在实数范围内进行彻底分解,
x^5+x^4+1=(x-a)(x^2+x+1)(x^2-bx+c)
其中a=x3,b=x4+x5,c=x4*x5

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