Question Number 166526 by mathlove last updated on 21/Feb/22
Answered by MJS_new last updated on 21/Feb/22
$$\Rightarrow \\ $$$${x}^{\mathrm{4}} +\frac{\mathrm{7}}{\mathrm{2}}{x}^{\mathrm{3}} +\frac{\mathrm{9}}{\mathrm{2}}{x}^{\mathrm{2}} +\frac{\mathrm{7}}{\mathrm{2}}{x}−\frac{\mathrm{5}}{\mathrm{2}}=\mathrm{0} \\ $$$$\left({x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +\frac{\mathrm{3}}{\mathrm{2}}{x}+\frac{\mathrm{5}}{\mathrm{2}}\right)=\mathrm{0} \\ $$$$\Rightarrow \\ $$$${x}=−\mathrm{1}\pm\sqrt{\mathrm{2}} \\ $$$${x}=−\frac{\mathrm{3}}{\mathrm{4}}\pm\frac{\sqrt{\mathrm{31}}}{\mathrm{4}}\mathrm{i} \\ $$