Լուծեք 1-824t^3+9016320t-11948032=0

$$1 - 824 t ^ { 3 } + 9016320 t - 11948032 = 0$$

Լուծել t-ի համար (complex solution)

$$t=-\frac{21218^{\frac{2}{3}}\left(-1230647193+\sqrt{1396563552410904196751}i\right)^{-\frac{1}{3}}\left(1+\sqrt{3}i\right)\left(103\left(-1230647193+\sqrt{1396563552410904196751}i\right)^{\frac{2}{3}}\left(-\sqrt{3}i-1\right)+3005440\times 21218^{\frac{2}{3}}\right)}{17483632}\approx -105.261051846-2.045501007 \cdot 10^{-14}i$$

$$t=\frac{21218^{\frac{2}{3}}\left(-1230647193+\sqrt{1396563552410904196751}i\right)^{-\frac{1}{3}}\left(103\left(-1230647193+\sqrt{1396563552410904196751}i\right)^{\frac{2}{3}}+1502720\times 21218^{\frac{2}{3}}\right)}{4370908}\approx 103.935683027-6.818336691 \cdot 10^{-15}i$$

$$t=-\frac{21218^{\frac{2}{3}}\left(-1230647193+\sqrt{1396563552410904196751}i\right)^{-\frac{1}{3}}\left(-\sqrt{3}i+1\right)\left(103\left(-1+\sqrt{3}i\right)\left(-1230647193+\sqrt{1396563552410904196751}i\right)^{\frac{2}{3}}+3005440\times 21218^{\frac{2}{3}}\right)}{17483632}\approx 1.325368819+3.358896429 \cdot 10^{-14}i$$

Լուծել t-ի համար

$$t=-\frac{16\sqrt{604610}\cos(\frac{\arccos(\frac{11948031\sqrt{604610}}{282270924800})}{3})}{103}\approx -105.261051846$$

$$t=\frac{8\sqrt{604610}\left(\sqrt{3}\sin(\frac{\arccos(\frac{11948031\sqrt{604610}}{282270924800})}{3})+\cos(\frac{\arccos(\frac{11948031\sqrt{604610}}{282270924800})}{3})\right)}{103}\approx 103.935683027$$

$$t=\frac{8\sqrt{604610}\left(-\sqrt{3}\sin(\frac{\arccos(\frac{11948031\sqrt{604610}}{282270924800})}{3})+\cos(\frac{\arccos(\frac{11948031\sqrt{604610}}{282270924800})}{3})\right)}{103}\approx 1.325368819$$