5000=-2600/left(1+xright)^3-2600/left(1+xright)^6 का समाधान करें

$$5000=- \frac{ 2600 }{ { \left(1+x \right) }^{ 3 } } - \frac{ 2600 }{ { \left(1+x \right) }^{ 6 } }$$

x के लिए हल करें (जटिल समाधान)

$$\left\{\begin{matrix}x=\frac{50^{\frac{2}{3}}\left(\sqrt[3]{-13+\sqrt{1131}i}-\sqrt[3]{50}\right)}{50}\approx -0.284252323+0.540231815i\text{, }&-1\neq \frac{50^{\frac{2}{3}}\sqrt[3]{-13+\sqrt{1131}i}}{50}-1\\x=-\frac{50^{\frac{2}{3}}\left(\sqrt[3]{-13+\sqrt{1131}i}\left(1+\sqrt{3}i\right)+2\sqrt[3]{50}\right)}{100}\approx -0.890019363-0.889971579i\text{, }&-1\neq -\frac{50^{\frac{2}{3}}\sqrt[3]{-13+\sqrt{1131}i}\left(1+\sqrt{3}i\right)}{100}-1\\x=\frac{50^{\frac{2}{3}}\left(\left(-1+\sqrt{3}i\right)\sqrt[3]{-13+\sqrt{1131}i}-2\sqrt[3]{50}\right)}{100}\approx -1.825728315+0.349739763i\text{, }&-1\neq \frac{50^{\frac{2}{3}}\left(-1+\sqrt{3}i\right)\sqrt[3]{-13+\sqrt{1131}i}}{100}-1\\x=\frac{50^{\frac{2}{3}}\left(\sqrt[3]{-\sqrt{1131}i-13}-\sqrt[3]{50}\right)}{50}\approx -0.890019363+0.889971579i\text{, }&-1\neq \frac{50^{\frac{2}{3}}\sqrt[3]{-\sqrt{1131}i-13}}{50}-1\\x=-\frac{50^{\frac{2}{3}}\left(\left(1+\sqrt{3}i\right)\sqrt[3]{-\sqrt{1131}i-13}+2\sqrt[3]{50}\right)}{100}\approx -0.284252323-0.540231815i\text{, }&-1\neq -\frac{50^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\sqrt[3]{-\sqrt{1131}i-13}}{100}-1\\x=\frac{50^{\frac{2}{3}}\left(\left(-1+\sqrt{3}i\right)\sqrt[3]{-\sqrt{1131}i-13}-2\sqrt[3]{50}\right)}{100}\approx -1.825728315-0.349739763i\text{, }&-1\neq \frac{50^{\frac{2}{3}}\left(-1+\sqrt{3}i\right)\sqrt[3]{-\sqrt{1131}i-13}}{100}-1\end{matrix}\right.$$