Question

evaluate x3+1/x3 if x=2+2root3

Answer 1

Dear student,

$$\begin{gathered} x^3+\frac{1}{x^3},forx=2+2\sqrt{3} \\ \Rightarrow (2+2\sqrt{3}{)}^3+\hspace{0.17em}\frac{1}{(2+2\sqrt{3}{)}^3}=\frac{(2+2\sqrt{3}{)}^3*(2+2\sqrt{3}{)}^3+1}{(2+2\sqrt{3}{)}^3}=\frac{512(26+15\sqrt{3})+1}{16(5+3\sqrt{3})}=\frac{13313+7680\sqrt{3}}{16(5+3\sqrt{3})}=163.14456 \end{gathered}$$

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