Leysa x^14+y^4=1

$$x ^ { 14 } + y ^ { 4 } = 1$$

Leystu fyrir x (complex solution)

$$x\in e^{\frac{\pi i}{7}}\sqrt[14]{1-y^{4}},\sqrt[14]{1-y^{4}},e^{\frac{2i\pi }{7}}\sqrt[14]{1-y^{4}},e^{\frac{3i\pi }{7}}\sqrt[14]{1-y^{4}},e^{\frac{4i\pi }{7}}\sqrt[14]{1-y^{4}},e^{\frac{5i\pi }{7}}\sqrt[14]{1-y^{4}},e^{\frac{6i\pi }{7}}\sqrt[14]{1-y^{4}},-\sqrt[14]{1-y^{4}},e^{\frac{8i\pi }{7}}\sqrt[14]{1-y^{4}},e^{\frac{9i\pi }{7}}\sqrt[14]{1-y^{4}},e^{\frac{10i\pi }{7}}\sqrt[14]{1-y^{4}},e^{\frac{11i\pi }{7}}\sqrt[14]{1-y^{4}},e^{\frac{12i\pi }{7}}\sqrt[14]{1-y^{4}},e^{\frac{13i\pi }{7}}\sqrt[14]{1-y^{4}}$$

Leystu fyrir y (complex solution)

$$y=i\sqrt[4]{1-x^{14}}$$

$$y=\sqrt[4]{1-x^{14}}$$

$$y=-\sqrt[4]{1-x^{14}}$$

$$y=-i\sqrt[4]{1-x^{14}}$$

Leystu fyrir x

$$x=\sqrt[14]{1-y^{4}}$$

$$x=-\sqrt[14]{1-y^{4}}\text{, }|y|\leq 1$$

Leystu fyrir y

$$\left\{\begin{matrix}y=\sqrt{-\sqrt{1-x^{14}}}\text{; }y=-\sqrt{-\sqrt{1-x^{14}}}\text{, }&|x|=1\\y=\sqrt[4]{1-x^{14}}\text{; }y=-\sqrt[4]{1-x^{14}}\text{, }&|x|\leq 1\end{matrix}\right.$$