Vyriešiť 36x^6-81y^4=(6

$$36 x ^ { 6 } - 81 y ^ { 4 } = ( 6$$

Riešenie pre x (complex solution)

$$x\in \frac{12^{\frac{5}{6}}e^{\frac{\pi i}{3}}\sqrt[6]{27y^{4}+2}}{12},\frac{12^{\frac{5}{6}}\sqrt[6]{27y^{4}+2}}{12},\frac{12^{\frac{5}{6}}e^{\frac{2\pi i}{3}}\sqrt[6]{27y^{4}+2}}{12},-\frac{12^{\frac{5}{6}}\sqrt[6]{27y^{4}+2}}{12},\frac{12^{\frac{5}{6}}e^{\frac{4\pi i}{3}}\sqrt[6]{27y^{4}+2}}{12},\frac{12^{\frac{5}{6}}e^{\frac{5\pi i}{3}}\sqrt[6]{27y^{4}+2}}{12}$$

Riešenie pre y (complex solution)

$$y=\frac{i\sqrt[4]{36x^{6}-6}}{3}$$

$$y=\frac{\sqrt[4]{36x^{6}-6}}{3}$$

$$y=-\frac{\sqrt[4]{36x^{6}-6}}{3}$$

$$y=-\frac{i\sqrt[4]{36x^{6}-6}}{3}$$

Riešenie pre x

$$x=\frac{12^{\frac{5}{6}}\sqrt[6]{27y^{4}+2}}{12}$$

$$x=-\frac{12^{\frac{5}{6}}\sqrt[6]{27y^{4}+2}}{12}$$

Riešenie pre y

$$\left\{\begin{matrix}y=\frac{\sqrt[4]{6}\sqrt{-\sqrt{6x^{6}-1}}}{3}\text{; }y=-\frac{\sqrt[4]{6}\sqrt{-\sqrt{6x^{6}-1}}}{3}\text{, }&|x|=\frac{6^{\frac{5}{6}}}{6}\\y=\frac{\sqrt[4]{36x^{6}-6}}{3}\text{; }y=-\frac{\sqrt[4]{36x^{6}-6}}{3}\text{, }&|x|\geq \frac{6^{\frac{5}{6}}}{6}\end{matrix}\right,$$