25x^2/y-46y^2/x=xy का समाधान करें

$$\frac { 25 x ^ { 2 } } { y } - \frac { 46 y ^ { 2 } } { x } = x y$$

x के लिए हल करें

$$x=-\frac{\sqrt{3}i\left(y^{6}+75\sqrt{138y^{9}[phone]y^{6}}+388125y^{3}\right)^{-\frac{1}{3}}y^{4}}{150}+\frac{\sqrt{3}i\sqrt[3]{y^{6}+75\sqrt{138y^{9}[phone]y^{6}}+388125y^{3}}}{150}-\frac{\sqrt[3]{y^{6}+75\sqrt{138y^{9}[phone]y^{6}}+388125y^{3}}}{150}+\frac{y^{2}}{75}-\frac{\left(y^{6}+75\sqrt{138y^{9}[phone]y^{6}}+388125y^{3}\right)^{-\frac{1}{3}}y^{4}}{150}$$

$$x=\frac{\sqrt[3]{y^{6}+75\sqrt{138y^{9}[phone]y^{6}}+388125y^{3}}+y^{2}+\left(y^{6}+75\sqrt{138y^{9}[phone]y^{6}}+388125y^{3}\right)^{-\frac{1}{3}}y^{4}}{75}$$

$$x=\frac{\sqrt{3}i\left(y^{6}+75\sqrt{138y^{9}[phone]y^{6}}+388125y^{3}\right)^{-\frac{1}{3}}y^{4}}{150}-\frac{\sqrt{3}i\sqrt[3]{y^{6}+75\sqrt{138y^{9}[phone]y^{6}}+388125y^{3}}}{150}-\frac{\sqrt[3]{y^{6}+75\sqrt{138y^{9}[phone]y^{6}}+388125y^{3}}}{150}+\frac{y^{2}}{75}-\frac{\left(y^{6}+75\sqrt{138y^{9}[phone]y^{6}}+388125y^{3}\right)^{-\frac{1}{3}}y^{4}}{150}\text{, }y\neq 0$$

y के लिए हल करें

$$y=-\frac{\sqrt{3}i\left(-x^{6}+690\sqrt{1071225x^{6}-3x^{9}}+714150x^{3}\right)^{-\frac{1}{3}}x^{4}}{276}+\frac{\sqrt{3}i\sqrt[3]{-x^{6}+690\sqrt{1071225x^{6}-3x^{9}}+714150x^{3}}}{276}-\frac{\sqrt[3]{-x^{6}+690\sqrt{1071225x^{6}-3x^{9}}+714150x^{3}}}{276}-\frac{x^{2}}{138}-\frac{\left(-x^{6}+690\sqrt{1071225x^{6}-3x^{9}}+714150x^{3}\right)^{-\frac{1}{3}}x^{4}}{276}$$

$$y=\frac{\sqrt[3]{-x^{6}+690\sqrt{1071225x^{6}-3x^{9}}+714150x^{3}}-x^{2}+\left(-x^{6}+690\sqrt{1071225x^{6}-3x^{9}}+714150x^{3}\right)^{-\frac{1}{3}}x^{4}}{138}$$

$$y=\frac{\sqrt{3}i\left(-x^{6}+690\sqrt{1071225x^{6}-3x^{9}}+714150x^{3}\right)^{-\frac{1}{3}}x^{4}}{276}-\frac{\sqrt{3}i\sqrt[3]{-x^{6}+690\sqrt{1071225x^{6}-3x^{9}}+714150x^{3}}}{276}-\frac{\sqrt[3]{-x^{6}+690\sqrt{1071225x^{6}-3x^{9}}+714150x^{3}}}{276}-\frac{x^{2}}{138}-\frac{\left(-x^{6}+690\sqrt{1071225x^{6}-3x^{9}}+714150x^{3}\right)^{-\frac{1}{3}}x^{4}}{276}\text{, }x\neq 0$$