a) $x + 2\sqrt{2x - 4} = 2 + 2\sqrt{2(x - 2)} + x - 2 = (\sqrt{2})^{2} + 2.\sqrt{2}.\sqrt{x - 2} + (\sqrt{x - 2})^{2} = (\sqrt{2} + \sqrt{x - 2})^{2}$
b) $\sqrt{x + 2\sqrt{2x - 4}} + \sqrt{x - 2\sqrt{2x - 4}} = \sqrt{(\sqrt{2} + \sqrt{x - 2})^{2}} + \sqrt{(\sqrt{2} - \sqrt{x - 2})^{2}} = \sqrt{2} + \sqrt{x - 2} + \sqrt{2} - \sqrt{x - 2} = 2\sqrt{2}$