Question

if x⁴+1/x⁴=47 find the value of x+1/x

Answer 1

Dear student
$$\begin{gathered} {\mathrm{x}}^4+\frac{1}{{\mathrm{x}}^4}=47 \\ \mathrm{We}\mathrm{know}\mathrm{that} \\ {\left({\mathrm{x}}^2+\frac{1}{{\mathrm{x}}^2}\right)}^2={\mathrm{x}}^4+\frac{1}{{\mathrm{x}}^4}+2=47+2=49 \\ \mathrm{So},{\left({\mathrm{x}}^2+\frac{1}{{\mathrm{x}}^2}\right)}^2=49 \\ \Rightarrow {\mathrm{x}}^2+\frac{1}{{\mathrm{x}}^2}=7 \\ \Rightarrow {\left(\mathrm{x}+\frac{1}{\mathrm{x}}\right)}^2-2=7 \\ \Rightarrow {\left(\mathrm{x}+\frac{1}{\mathrm{x}}\right)}^2=9 \\ \Rightarrow \mathrm{x}+\frac{1}{\mathrm{x}}=3 \end{gathered}$$
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