15y^12+6x^3=0 का समाधान करें

$$15 y ^ { 12 } + 6 x ^ { 3 } = 0$$

x के लिए हल करें (जटिल समाधान)

$$x=-\frac{\sqrt[3]{5}\times 2^{\frac{2}{3}}y^{4}}{2}$$

$$x=\frac{\sqrt[3]{5}\times 2^{\frac{2}{3}}e^{\frac{\pi i}{3}}y^{4}}{2}$$

$$x=\frac{\sqrt[3]{5}\times 2^{\frac{2}{3}}e^{\frac{5\pi i}{3}}y^{4}}{2}$$

y के लिए हल करें (जटिल समाधान)

$$y\in 2^{\frac{7}{12}}\times 5^{\frac{11}{12}}\left(\frac{1}{10}+\frac{1}{10}i\right)\sqrt[4]{x},\frac{5^{\frac{11}{12}}\sqrt[12]{2}e^{\frac{\pi i}{12}}\sqrt[4]{x}}{5},\frac{5^{\frac{11}{12}}\sqrt[12]{2}e^{\frac{5\pi i}{12}}\sqrt[4]{x}}{5},\frac{5^{\frac{11}{12}}\sqrt[12]{2}e^{\frac{7\pi i}{12}}\sqrt[4]{x}}{5},2^{\frac{7}{12}}\times 5^{\frac{11}{12}}\left(-\frac{1}{10}+\frac{1}{10}i\right)\sqrt[4]{x},\frac{5^{\frac{11}{12}}\sqrt[12]{2}e^{\frac{11\pi i}{12}}\sqrt[4]{x}}{5},\frac{5^{\frac{11}{12}}\sqrt[12]{2}e^{\frac{13\pi i}{12}}\sqrt[4]{x}}{5},2^{\frac{7}{12}}\times 5^{\frac{11}{12}}\left(-\frac{1}{10}-\frac{1}{10}i\right)\sqrt[4]{x},\frac{5^{\frac{11}{12}}\sqrt[12]{2}e^{\frac{17\pi i}{12}}\sqrt[4]{x}}{5},\frac{5^{\frac{11}{12}}\sqrt[12]{2}e^{\frac{19\pi i}{12}}\sqrt[4]{x}}{5},2^{\frac{7}{12}}\times 5^{\frac{11}{12}}\left(\frac{1}{10}-\frac{1}{10}i\right)\sqrt[4]{x},\frac{5^{\frac{11}{12}}\sqrt[12]{2}e^{\frac{23\pi i}{12}}\sqrt[4]{x}}{5}$$

x के लिए हल करें

$$x=-\frac{\sqrt[3]{5}\times 2^{\frac{2}{3}}y^{4}}{2}$$

y के लिए हल करें

$$y=\frac{5^{\frac{11}{12}}\sqrt[12]{-2x^{3}}}{5}$$

$$y=-\frac{5^{\frac{11}{12}}\sqrt[12]{-2x^{3}}}{5}\text{, }x\leq 0$$