{l}{x^3+y^3=9}{x^3-4y^3=12} का समाधान करें

$$\left. \begin{array} { l } { x ^ { 3 } + y ^ { 3 } = 9 } \\ { x ^ { 3 } - 4 y ^ { 3 } = 12 } \end{array} \right.$$

x, y के लिए हल करें (जटिल समाधान)

$$x=\frac{2\sqrt[3]{6}\times 5^{\frac{2}{3}}}{5}\approx 2.125317138\text{, }y=\frac{\sqrt[3]{3}\times 5^{\frac{2}{3}}e^{\frac{\pi i}{3}}}{5}\approx 0.421716333+0.730434115i$$

$$x=\frac{2\sqrt[3]{6}\times 5^{\frac{2}{3}}}{5}\approx 2.125317138\text{, }y=-\frac{\sqrt[3]{3}\times 5^{\frac{2}{3}}}{5}\approx -0.843432665$$

$$x=\frac{2\sqrt[3]{6}\times 5^{\frac{2}{3}}}{5}\approx 2.125317138\text{, }y=\frac{\sqrt[3]{3}\times 5^{\frac{2}{3}}e^{\frac{5\pi i}{3}}}{5}\approx 0.421716333-0.730434115i$$

$$x=\frac{2\sqrt[3]{6}\times 5^{\frac{2}{3}}e^{\frac{2\pi i}{3}}}{5}\approx -1.062658569+1.840578633i\text{, }y=\frac{\sqrt[3]{3}\times 5^{\frac{2}{3}}e^{\frac{\pi i}{3}}}{5}\approx 0.421716333+0.730434115i$$

$$x=\frac{2\sqrt[3]{6}\times 5^{\frac{2}{3}}e^{\frac{2\pi i}{3}}}{5}\approx -1.062658569+1.840578633i\text{, }y=-\frac{\sqrt[3]{3}\times 5^{\frac{2}{3}}}{5}\approx -0.843432665$$

$$x=\frac{2\sqrt[3]{6}\times 5^{\frac{2}{3}}e^{\frac{2\pi i}{3}}}{5}\approx -1.062658569+1.840578633i\text{, }y=\frac{\sqrt[3]{3}\times 5^{\frac{2}{3}}e^{\frac{5\pi i}{3}}}{5}\approx 0.421716333-0.730434115i$$

$$x=\frac{2\sqrt[3]{6}\times 5^{\frac{2}{3}}e^{\frac{4\pi i}{3}}}{5}\approx -1.062658569-1.840578633i\text{, }y=\frac{\sqrt[3]{3}\times 5^{\frac{2}{3}}e^{\frac{\pi i}{3}}}{5}\approx 0.421716333+0.730434115i$$

$$x=\frac{2\sqrt[3]{6}\times 5^{\frac{2}{3}}e^{\frac{4\pi i}{3}}}{5}\approx -1.062658569-1.840578633i\text{, }y=-\frac{\sqrt[3]{3}\times 5^{\frac{2}{3}}}{5}\approx -0.843432665$$

$$x=\frac{2\sqrt[3]{6}\times 5^{\frac{2}{3}}e^{\frac{4\pi i}{3}}}{5}\approx -1.062658569-1.840578633i\text{, }y=\frac{\sqrt[3]{3}\times 5^{\frac{2}{3}}e^{\frac{5\pi i}{3}}}{5}\approx 0.421716333-0.730434115i$$

x, y के लिए हल करें

$$x = \frac{2 \sqrt[3]{6} \cdot 5 ^ {\frac{2}{3}}}{5} \approx 2.125317138$$

$$y=-\frac{\sqrt[3]{3}\times 5^{\frac{2}{3}}}{5}\approx -0.843432665$$