解決x^3-7x=-42 |Microsoft數學求解器

$$x ^ { 3 } - 7 x = - 42$$

解 x (復數求解)

$$x=-\frac{\sqrt[3]{7}\times 9^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(-\sqrt{3}\sqrt[3]{2\sqrt{177}-27}i-\sqrt[3]{2\sqrt{177}-27}+2\sqrt[3]{-2\sqrt{177}-27}\right)}{36}\approx 1.06090486-3.003030462i$$

$$x=\frac{\sqrt[3]{7}\times 9^{\frac{2}{3}}\left(\sqrt[3]{2\sqrt{177}-27}+\sqrt[3]{-2\sqrt{177}-27}\right)}{9}\approx 2.070248239+3.585775134i$$

$$x=-\frac{\sqrt[3]{7}\times 9^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(-\sqrt[3]{2\sqrt{177}-27}+2\sqrt[3]{-2\sqrt{177}-27}+\sqrt{3}\sqrt[3]{2\sqrt{177}-27}i\right)}{36}\approx -3.131153099-0.582744671i$$

解 x

$$x = -\frac{\sqrt[3]{7} \cdot 9 ^ {\frac{2}{3}} {(\sqrt[3]{2 \sqrt{177} + 27} + \sqrt[3]{27 - 2 \sqrt{177}})}}{9} \approx -4.140496478$$