8x^2y^3-5x^2+7y^3=10x-30y хәл итегез

$$8 x ^ { 2 } y ^ { 3 } - 5 x ^ { 2 } + 7 y ^ { 3 } = 10 x - 30 y$$

x өчен чишелеш (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{25+150y+35y^{3}-240y^{4}-56y^{6}}+5}{8y^{3}-5}\text{; }x=\frac{-\sqrt{25+150y+35y^{3}-240y^{4}-56y^{6}}+5}{8y^{3}-5}\text{, }&y\neq \frac{\sqrt[3]{5}}{2}\text{ and }y\neq \frac{\sqrt[3]{5}e^{\frac{4\pi i}{3}}}{2}\text{ and }y\neq \frac{\sqrt[3]{5}e^{\frac{2\pi i}{3}}}{2}\\x=\frac{y\left(7y^{2}+30\right)}{10}\text{, }&y=\frac{\sqrt[3]{5}e^{\frac{4\pi i}{3}}}{2}\text{ or }y=\frac{\sqrt[3]{5}e^{\frac{2\pi i}{3}}}{2}\text{ or }y=\frac{\sqrt[3]{5}}{2}\end{matrix}\right.$$

x өчен чишелеш

$$\left\{\begin{matrix}x=\frac{\sqrt{25+150y+35y^{3}-240y^{4}-56y^{6}}+5}{8y^{3}-5}\text{; }x=\frac{-\sqrt{25+150y+35y^{3}-240y^{4}-56y^{6}}+5}{8y^{3}-5}\text{, }&y\neq \frac{\sqrt[3]{5}}{2}\text{ and }25+150y+35y^{3}-240y^{4}-56y^{6}\geq 0\\x=\frac{24\sqrt[3]{5}+7}{16}\text{, }&y=\frac{\sqrt[3]{5}}{2}\end{matrix}\right.$$

y өчен чишелеш

$$y=\frac{\sqrt[3]{5}\times 2^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{8x^{2}+7}x^{2}+\sqrt{8x^{6}+32x^{5}+39x^{4}+28x^{3}+28x^{2}+160}+2x\sqrt{8x^{2}+7}}+\sqrt[3]{\sqrt{8x^{2}+7}x^{2}-\sqrt{8x^{6}+32x^{5}+39x^{4}+28x^{3}+28x^{2}+160}+2x\sqrt{8x^{2}+7}}\right)}{2\sqrt{8x^{2}+7}}$$