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Question Number 163860 by mathlove last updated on 11/Jan/22

Answered by Ar Brandon last updated on 11/Jan/22

⇒(x)^(1/4) +(1/( (x)^(1/4) ))+(x)^(1/4) +(1/( (x)^(1/4) ))=5  ⇒2(x)^(1/4) +(2/( (x)^(1/4) ))=5  ⇒2(x^2 )^(1/4) −5(x)^(1/4) +2=0  ⇒(x)^(1/4) =((5±(√9))/4)  ⇒x=(((5±3)^4 )/(16))

$$\Rightarrow\sqrt[{\mathrm{4}}]{{x}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{{x}}}+\sqrt[{\mathrm{4}}]{{x}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{{x}}}=\mathrm{5} \\ $$$$\Rightarrow\mathrm{2}\sqrt[{\mathrm{4}}]{{x}}+\frac{\mathrm{2}}{\:\sqrt[{\mathrm{4}}]{{x}}}=\mathrm{5} \\ $$$$\Rightarrow\mathrm{2}\sqrt[{\mathrm{4}}]{{x}^{\mathrm{2}} }−\mathrm{5}\sqrt[{\mathrm{4}}]{{x}}+\mathrm{2}=\mathrm{0} \\ $$$$\Rightarrow\sqrt[{\mathrm{4}}]{{x}}=\frac{\mathrm{5}\pm\sqrt{\mathrm{9}}}{\mathrm{4}} \\ $$$$\Rightarrow{x}=\frac{\left(\mathrm{5}\pm\mathrm{3}\right)^{\mathrm{4}} }{\mathrm{16}} \\ $$

Commented by mathlove last updated on 11/Jan/22

thanks

$${thanks} \\ $$

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