Question Number 163860 by mathlove last updated on 11/Jan/22
Answered by Ar Brandon last updated on 11/Jan/22
$$\Rightarrow\sqrt[{\mathrm{4}}]{{x}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{{x}}}+\sqrt[{\mathrm{4}}]{{x}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{{x}}}=\mathrm{5} \\ $$$$\Rightarrow\mathrm{2}\sqrt[{\mathrm{4}}]{{x}}+\frac{\mathrm{2}}{\:\sqrt[{\mathrm{4}}]{{x}}}=\mathrm{5} \\ $$$$\Rightarrow\mathrm{2}\sqrt[{\mathrm{4}}]{{x}^{\mathrm{2}} }−\mathrm{5}\sqrt[{\mathrm{4}}]{{x}}+\mathrm{2}=\mathrm{0} \\ $$$$\Rightarrow\sqrt[{\mathrm{4}}]{{x}}=\frac{\mathrm{5}\pm\sqrt{\mathrm{9}}}{\mathrm{4}} \\ $$$$\Rightarrow{x}=\frac{\left(\mathrm{5}\pm\mathrm{3}\right)^{\mathrm{4}} }{\mathrm{16}} \\ $$
Commented by mathlove last updated on 11/Jan/22
$${thanks} \\ $$