Resol x^frac{8{3}}+8/y^3=1000

$$x ^ { \frac { 8 } { 3 } } + \frac { 8 } { y ^ { 3 } } = 1000$$

Resoleu x (complex solution)

$$x\in 2^{\frac{9}{8}}e^{\frac{3i\pi }{8}}y^{-\frac{9}{8}}\left(1-125y^{3}\right)^{\frac{3}{8}},2^{\frac{9}{8}}e^{\frac{\pi i}{8}}y^{-\frac{9}{8}}\left(1-125y^{3}\right)^{\frac{3}{8}},2^{\frac{9}{8}}e^{\frac{5i\pi }{8}}y^{-\frac{9}{8}}\left(1-125y^{3}\right)^{\frac{3}{8}},2^{\frac{9}{8}}e^{\frac{7i\pi }{8}}y^{-\frac{9}{8}}\left(1-125y^{3}\right)^{\frac{3}{8}},2^{\frac{9}{8}}e^{\frac{9i\pi }{8}}y^{-\frac{9}{8}}\left(1-125y^{3}\right)^{\frac{3}{8}},2^{\frac{9}{8}}e^{\frac{11i\pi }{8}}y^{-\frac{9}{8}}\left(1-125y^{3}\right)^{\frac{3}{8}},2^{\frac{9}{8}}e^{\frac{13i\pi }{8}}y^{-\frac{9}{8}}\left(1-125y^{3}\right)^{\frac{3}{8}},2^{\frac{9}{8}}e^{\frac{15i\pi }{8}}y^{-\frac{9}{8}}\left(1-125y^{3}\right)^{\frac{3}{8}}$$

$$y=\frac{1}{5}\text{ or }y=\frac{-\sqrt{3}i-1}{10}\text{ or }y=\frac{-1+\sqrt{3}i}{10}\text{ or }\left(y\neq 0\text{ and }arg(1000-\frac{8}{y^{3}})<\frac{2\pi }{3}\text{ and }y\neq \frac{1}{5}\text{ and }y\neq \frac{-\sqrt{3}i-1}{10}\text{ and }y\neq \frac{-1+\sqrt{3}i}{10}\right)$$

Resoleu y (complex solution)

$$y=-2\left(x^{\frac{8}{3}}-1000\right)^{-\frac{1}{3}}$$

$$y=2e^{\frac{\pi i}{3}}\left(x^{\frac{8}{3}}-1000\right)^{-\frac{1}{3}}$$

$$y=2e^{\frac{5\pi i}{3}}\left(x^{\frac{8}{3}}-1000\right)^{-\frac{1}{3}}\text{, }x\neq -\sqrt[8]{10}\times \left(10i\right)\text{ and }x\neq \sqrt[8]{160}\left(-5+5i\right)\text{ and }x\neq 10^{\frac{9}{8}}$$

Resoleu x

$$x=2\sqrt[8]{-\frac{2\left(1-5y\right)^{3}}{y^{9}}}\left(25y^{2}+5y+1\right)^{\frac{3}{8}}$$

$$x=-2\sqrt[8]{-\frac{2\left(1-5y\right)^{3}}{y^{9}}}\left(25y^{2}+5y+1\right)^{\frac{3}{8}}\text{, }y<0\text{ or }y\geq \frac{1}{5}$$

Resoleu y

$$y=-\frac{2}{\sqrt[3]{x^{\frac{8}{3}}-1000}}$$

$$|x|\neq 10^{\frac{9}{8}}$$