x2+x+1=0x^2+x+1=0x2+x+1=0 一出现,就要搞事情。
1.(x−1)(x2+x+1)=x3−1=0,x3=1(x-1)(x^2+x+1)=x^3-1=0,x^3=1(x−1)(x2+x+1)=x3−1=0,x3=1
2.x4+x2+1=(x2+x+1)(x2−x+1)=0x^4+x^2+1=(x^2+x+1)(x^2-x+1)=0x4+x2+1=(x2+x+1)(x2−x+1)=0
3.x2+1=−x,x+1x=(x2+1)÷x=−1x^2+1=-x,x+\frac{1}{x}=(x^2+1)\div x=-1x2+1=−x,x+x1=(x2+1)÷x=−1
4.x4−x=x(x−1)(x2+x+1)=0x^4-x=x(x-1)(x^2+x+1)=0x4−x=x(x−1)(x2+x+1)=0
谢谢阅读