פתור את x^14+x^13+1/x^2+x+1=1

$$\frac{ { x }^{ 14 } + { x }^{ 13 } +1 }{ { x }^{ 2 } +x+1 } =1$$

פתור עבור x (complex solution)

$$\left\{\begin{matrix}\\x\in 1,0,\frac{-\sqrt{3}i+1}{2},\frac{1+\sqrt{3}i}{2},-i,i,-1\text{, }&\text{unconditionally}\\x=e^{\frac{5\pi i}{6}}\approx -0.866025404+0.5i\text{, }&e^{\frac{5\pi i}{6}}\neq \frac{-1+\sqrt{3}i}{2}\text{ and }e^{\frac{5\pi i}{6}}\neq \frac{-\sqrt{3}i-1}{2}\\x=e^{\frac{11\pi i}{6}}\approx 0.866025404-0.5i\text{, }&e^{\frac{11\pi i}{6}}\neq \frac{-1+\sqrt{3}i}{2}\text{ and }e^{\frac{11\pi i}{6}}\neq \frac{-\sqrt{3}i-1}{2}\\x=e^{\frac{\pi i}{6}}\approx 0.866025404+0.5i\text{, }&e^{\frac{\pi i}{6}}\neq \frac{-1+\sqrt{3}i}{2}\text{ and }e^{\frac{\pi i}{6}}\neq \frac{-\sqrt{3}i-1}{2}\\x=e^{\frac{7\pi i}{6}}\approx -0.866025404-0.5i\text{, }&e^{\frac{7\pi i}{6}}\neq \frac{-1+\sqrt{3}i}{2}\text{ and }e^{\frac{7\pi i}{6}}\neq \frac{-\sqrt{3}i-1}{2}\end{matrix}\right.$$

פתור עבור x

$$x=1$$

$$x=0$$

$$x=-1$$