Riješi 8x^18-729y^3=15

$$8 x ^ { 18 } - 729 y ^ { 3 } = 15$$

Riješite za x (complex solution)

$$x\in \frac{2^{\frac{5}{6}}e^{\frac{\pi i}{9}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}e^{\frac{2\pi i}{9}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}e^{\frac{\pi i}{3}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}e^{\frac{4\pi i}{9}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}e^{\frac{5\pi i}{9}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}e^{\frac{2\pi i}{3}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}e^{\frac{7\pi i}{9}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}e^{\frac{8\pi i}{9}}\sqrt[18]{729y^{3}+15}}{2},-\frac{2^{\frac{5}{6}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}e^{\frac{10\pi i}{9}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}e^{\frac{11\pi i}{9}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}e^{\frac{4\pi i}{3}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}e^{\frac{13\pi i}{9}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}e^{\frac{14\pi i}{9}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}e^{\frac{5\pi i}{3}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}e^{\frac{16\pi i}{9}}\sqrt[18]{729y^{3}+15}}{2},\frac{2^{\frac{5}{6}}e^{\frac{17\pi i}{9}}\sqrt[18]{729y^{3}+15}}{2}$$

Riješite za y (complex solution)

$$y=\frac{e^{\frac{2\pi i}{3}}\sqrt[3]{8x^{18}-15}}{9}$$

$$y=\frac{\sqrt[3]{8x^{18}-15}}{9}$$

$$y=\frac{e^{\frac{4\pi i}{3}}\sqrt[3]{8x^{18}-15}}{9}$$

Riješite za x

$$x=\frac{2^{\frac{5}{6}}\sqrt[18]{729y^{3}+15}}{2}$$

$$x=-\frac{2^{\frac{5}{6}}\sqrt[18]{729y^{3}+15}}{2}\text{, }y\geq -\frac{\sqrt[3]{5}\times 9^{\frac{2}{3}}}{27}$$

Riješite za y

$$y=\frac{\sqrt[3]{8x^{18}-15}}{9}$$