Question Number 165751 by cortano1 last updated on 07/Feb/22
$$\:\mathrm{x}^{\mathrm{3}} +\mathrm{6x}−\mathrm{9}=\mathrm{0}\:\Rightarrow\mathrm{x}=? \\ $$
Answered by MJS_new last updated on 08/Feb/22
$${x}_{\mathrm{1}} =\sqrt[{\mathrm{3}}]{\frac{\mathrm{9}+\sqrt{\mathrm{113}}}{\mathrm{2}}}−\sqrt[{\mathrm{3}}]{\frac{−\mathrm{9}+\sqrt{\mathrm{113}}}{\mathrm{2}}}\approx\mathrm{1}.\mathrm{20695981419} \\ $$$${x}_{\mathrm{2}} =\omega\sqrt[{\mathrm{3}}]{\frac{\mathrm{9}+\sqrt{\mathrm{113}}}{\mathrm{2}}}−\omega^{\mathrm{2}} \sqrt[{\mathrm{3}}]{\frac{−\mathrm{9}+\sqrt{\mathrm{113}}}{\mathrm{2}}}\approx−.\mathrm{603479907094}+\mathrm{2}.\mathrm{66318681185i} \\ $$$${x}_{\mathrm{3}} =\omega^{\mathrm{2}} \sqrt[{\mathrm{3}}]{\frac{\mathrm{9}+\sqrt{\mathrm{113}}}{\mathrm{2}}}−\omega\sqrt[{\mathrm{3}}]{\frac{−\mathrm{9}+\sqrt{\mathrm{113}}}{\mathrm{2}}}\approx−.\mathrm{603479907094}−\mathrm{2}.\mathrm{66318681185i} \\ $$