x^3+2x^2+x+37=0 хәл итегез

$$x ^ { 3 } + 2 x ^ { 2 } + x + 37 = 0$$

x өчен чишелеш (complex solution)

$$x=-\frac{2^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(-\sqrt{3}\sqrt[3]{3\sqrt{110445}-997}i-2\sqrt{3}\sqrt[3]{2}i-\sqrt[3]{3\sqrt{110445}-997}+2\sqrt[3]{-3\sqrt{110445}-997}+2\sqrt[3]{2}\right)}{24}\approx 0.964964361-2.883860736i$$

$$x=\frac{2^{\frac{2}{3}}\left(\sqrt[3]{3\sqrt{110445}-997}+\sqrt[3]{-3\sqrt{110445}-997}-2\sqrt[3]{2}\right)}{6}\approx 1.015014478+2.912757184i$$

$$x=-\frac{2^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(-\sqrt[3]{3\sqrt{110445}-997}+2\sqrt[3]{-3\sqrt{110445}-997}+2\sqrt[3]{2}+\sqrt{3}\sqrt[3]{3\sqrt{110445}-997}i+2\sqrt{3}\sqrt[3]{2}i\right)}{24}\approx -3.979978839-0.028896449i$$

x өчен чишелеш

$$x=-\frac{2^{\frac{2}{3}}\sqrt[3]{3\sqrt{110445}+997}}{6}-\frac{2^{\frac{2}{3}}\sqrt[3]{997-3\sqrt{110445}}}{6}-\frac{2}{3}\approx -4.030028956$$