For the following questions answer them individually
If $$x = \left(\sqrt2 - 1\right)^{-\frac{1}{2}}$$ then the value of $$\left(x^2 - \frac{1}{x^2}\right)$$ is
$$\frac{3}{4}\left(1 + \frac{1}{3}\right)\left(1 + \frac{2}{3}\right)\left(1 - \frac{2}{5}\right)\left(1 + \frac{6}{7}\right)\left(1 - \frac{12}{13}\right)$$ is equal to
The largest among the numbers $$\sqrt{7} - \sqrt{5}, \sqrt{5} - \sqrt{3}, \sqrt{9} - \sqrt{7}, \sqrt{11} - \sqrt{9}$$ is
If $$x^{\frac{1}{3}} + y^{\frac{1}{3}} = z^{\frac{1}{3}}$$, then $$(x + y - z)^3 + 27 xyz$$ is equal to
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