Question

x=√2-1 ... find (x-1/x)^3+3(x-1/x)+2​

Answer 1

Answer:

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$=(1−2)(1+2)1+2</p><p>\begin{gathered}=\frac{1+\sqrt{2}}{1^{2}-(\sqrt{2})^{2}}\\=\frac{1+\sqrt{2}}{1-2}\\=-(1+\sqrt{2})\:--(2)\end{gathered}=12−(2)21+2=1−21+2=−(1+2)−−(2)</p><p>\begin{gathered}Now,\\\left(x-\frac{1}{x}\right)^{3}\\=\left(1-\sqrt{2}-[-(1+\sqrt{2})]\right)^{3}\\=\left(1-\sqrt{2}+1+\sqrt{2}\right)^{3}\\=2^{3}\\=8\end{gathered}Now,(x−x1)3=(1−2−[−(1+2)])3=(1−2+1+2)3=23=8</p><p>Therefore,</p><p>\left(x-\frac{1}{x}\right)^{3}=8(x−x1)3=8</p><p>$

Answer 2

Answer:

Answer is Given in Attachment

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@ItzDazzingBoy(Rishab)