Question 51

If $$x = \left(\sqrt2 - 1\right)^{-\frac{1}{2}}$$ then the value of $$\left(x^2 - \frac{1}{x^2}\right)$$ is

Solution

$$x = \left(\sqrt2 - 1\right)^{-\frac{1}{2}} = \frac{1}{\sqrt{\sqrt{2} -1}} $$

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

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

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

solving = 2

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