Question

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Answer 1

Answer:

8

Step-by-step explanation:

$Given: x = 1 + \sqrt{2}$

Now:

$\Longrightarrow \frac{1}{x} = (\frac{1}{1+\sqrt{2}})$

$\Longrightarrow (\frac{1}{1+\sqrt{2}}) \ * \ \frac{({1-\sqrt{2})}}{(1-\sqrt{2})}$

$\Longrightarrow \frac{1-\sqrt{2}}{(1)^2 - (\sqrt{2})^2}$

$\Longrightarrow \frac{1-\sqrt{2}}{1-2}$

$\Longrightarrow \frac{1-\sqrt{2}}{-1}$

$\Longrightarrow \sqrt{2} - 1$

Then:

$\Longrightarrow (x - \frac{1}{x})^3$

$\Longrightarrow (1 + \sqrt{2} - \sqrt{2} + 1)^3$

$\Longrightarrow (2)^3$

$\Longrightarrow \textbf 8$

Hope it helps!

Answer 2

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