Question 115

If x = 1 - √2 , then the value of $$(x - 1/x)^3$$

Solution

Expression : $$x = 1 - \sqrt{2}$$

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

=> $$\frac{1}{x} = \frac{1}{1 - \sqrt{2}} \times \frac{1 + \sqrt{2}}{1 + \sqrt{2}}$$

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

To find : $$(x - \frac{1}{x})^3$$

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

= $$2^3 = 8$$

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