Question 115

If x = 1 - √2 , the value of $$(x-\frac{1}{x})^{3}$$ is

Solution

x = 1 -$$\sqrt{2}$$,

$$\frac{1}{x}=\frac{1}{1-\sqrt{2}}$$

= $$\frac{1}{1-\sqrt{2}}$$ X $$\frac{1+\sqrt{2}}{1+\sqrt{2}}$$

= -1 - $$\sqrt{2}$$

$$(x-\frac{1}{x})^{3}$$ = $$(1-\sqrt{2}-(-1-\sqrt{2}))^{3}$$=$$(2)^{3}$$=8.

so the answer is option B.

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