[tex]x = \frac{1}{ \sqrt{2} + 1} \\ x = \frac{ \sqrt{2} - 1 }{1} \\ x = \sqrt{2} - 1 \\ \\ \\ y = ( \frac{1}{2 \sqrt{3} } - \frac{1}{3 \sqrt{2} } - \frac{ \sqrt{3} + 1 }{6} ) \times \frac{1}{6} {}^{ - 1} \\y = \frac{ \sqrt{3} - \sqrt{2} - \sqrt{3} - 1 }{6} \times 6 \\ y = \frac{ \sqrt{2} + 1 }{ -6} \times \frac{6}{1} \\ y = \sqrt{2} + 1 \\ \\ \\ mg = \sqrt{x \times y} \\ mg = \sqrt{( \sqrt{2} - 1)( \sqrt{2} + 1) } \\ mg = \sqrt{( \sqrt{2}) {}^{2} - 1 {}^{2} } \\ mg = \sqrt{2 - 1} \\ mg = \sqrt{1 } \\ mg = 1[/tex]
