(x*i)x^2-(sqrt{3}+2)x+2sqrt{3}=0 സോൾവ് ചെയ്യുക

$$( x \times i ) x ^ { 2 } - ( \sqrt { 3 } + 2 ) x + 2 \sqrt { 3 } = 0$$

x എന്നതിനായി സോൾവ് ചെയ്യുക

$$x=\frac{\sqrt[3]{9}\times 3^{\frac{5}{6}}\left(1+\sqrt{3}i\right)\left(\sqrt{-15\sqrt{3}i+\left(-81-26i\right)}+9i\right)^{-\frac{1}{3}}\left(3\times 3^{\frac{5}{6}}i\times \left(\frac{\sqrt{-15\sqrt{3}i+\left(-81-26i\right)}+9i}{9}\right)^{\frac{2}{3}}+3\sqrt[3]{3}\times \left(\frac{\sqrt{-15\sqrt{3}i+\left(-81-26i\right)}+9i}{9}\right)^{\frac{2}{3}}+2\sqrt{3}i+4i\right)}{36}\approx -1.73261312+1.421793957i$$

$$x=\frac{\sqrt[3]{9}\times 3^{\frac{5}{6}}\left(\sqrt{-15\sqrt{3}i+\left(-81-26i\right)}+9i\right)^{-\frac{1}{3}}\left(3\sqrt[3]{3}\times \left(\frac{\sqrt{-15\sqrt{3}i+\left(-81-26i\right)}+9i}{9}\right)^{\frac{2}{3}}-\sqrt{3}i-2i\right)}{9}\approx 0.844784635+0.146891351i$$

$$x=-\frac{\sqrt[3]{9}\times 3^{\frac{5}{6}}\left(-\sqrt{3}i+1\right)\left(\sqrt{-15\sqrt{3}i+\left(-81-26i\right)}+9i\right)^{-\frac{1}{3}}\left(3\times 3^{\frac{5}{6}}i\times \left(\frac{\sqrt{-15\sqrt{3}i+\left(-81-26i\right)}+9i}{9}\right)^{\frac{2}{3}}-3\sqrt[3]{3}\times \left(\frac{\sqrt{-15\sqrt{3}i+\left(-81-26i\right)}+9i}{9}\right)^{\frac{2}{3}}-2\sqrt{3}i-4i\right)}{36}\approx 0.887828485-1.568685308i$$