已知x^2+x+1=0求有理式x^14+1/(x^14)的值

熱心網友

解：因為x^2+x+1=0，所以，兩邊都乘以x-1,得(x-1)(x^2+x+1)=0,x^3-1=0,即x^3=1.所以，x^14=(x^3)^4×x^2=1×x^2=x^2,1/(x^14)=1/x^2.所以，x^14+1/(x^14)=x^2+1/x^2=(x+1/x)^2-2.因為x^2+x+1=0，所以，兩邊都除以x,得x+1+1/x=0,即x+1/x=-1.所以x^14+1/(x^14)=(-1)^2-2=-1.

熱心網友

已知x^2+x+1=0求有理式x^14+1/(x^14)的值x^2+x+1=0顯然方程的解是虛數所以x+1/x=-1你還是初中吧那就用初中的方法x^3-1=(x-1)(x^2+x+1)=0x^3=1x^14+1/(x^14)=(x^3)^4*x^2+1/(x^3)^4*x^2=x^2+1/x^2=(x+1/x)^2-2=-1法2:x=cos120+sin120i或x=cos240+sin240ix^14+1/(x^14)=cos1680+sin1680i+cos-1680+sin-1680i=2cos1680=2cos240=-1或x^14+1/(x^14)=cos3360+sin3360i+cos-3360+sin-3360i=2cos3360=2cos120=-1suoyix^14+1/(x^14)=-1

熱心網友

判別式<0x無解