Răspuns:
[tex]a)a = \frac{1}{ \sqrt{2} + 1} = \frac{ \sqrt{2} - 1}{( \sqrt{2} + 1)( \sqrt{2} - 1)} = \frac{ \sqrt{2} - 1}{( { \sqrt{2}) }^{2} - {1}^{2} } \\ a = \frac{ \sqrt{2} - 1 }{2 - 1} \\ a = \sqrt{2} - 1[/tex]
[tex]b = | \frac{1}{2 \sqrt{3} } - \frac{1}{3 \sqrt{2} } - \frac{ \sqrt{3} + 1}{6} | \times ( \frac{1}{6} ) ^{ - 1} \\ b = | \frac{ \sqrt{3} }{2 \sqrt{3} \times \sqrt{3} } - \frac{ \sqrt{2} }{3 \sqrt{2} \times \sqrt{2} } - \frac{ \sqrt{3} + 1}{6} | \times {6}^{1} \\ b = | \frac{ \sqrt{3} }{6} - \frac{ \sqrt{2} }{6} - \frac{ \sqrt{3} + 1}{6} | \times 6 \\ b = | \frac{ \sqrt{3} - \sqrt{2} - \sqrt{3} - 1 }{6} | \times 6 \\ b = | \frac{ - \sqrt{2} - 1}{6} | \times 6 \\ b = | \frac{ - \sqrt{2} - \sqrt{1} }{6} | \times 6 \\ cum \: \: \sqrt{2} > \sqrt{1} \: rezulta \: ca \: | \frac{ - \sqrt{2} - \sqrt{1} }{6} | > 0 \: rezulta \: ca \: b = \frac{ - \sqrt{2} - \sqrt{1} }{6} \times 6 \\ b = - \sqrt{2} - \sqrt{1} \\ mg = \sqrt{a \times b} = \sqrt{( \sqrt{2} - 1) \times ( - \sqrt{2} - 1)} = \sqrt{2 - \sqrt{2} + \sqrt{2} + 1 } = \sqrt{3} [/tex]
[tex]b)b = | \frac{1}{2 \sqrt{5} } + \frac{1}{5 \sqrt{2} } - \frac{ \sqrt{5} + 2}{10} | \times ( - 10) \\ b = | \frac{ \sqrt{5} }{2 \sqrt{5} \times \sqrt{5} } + \frac{ \sqrt{2} }{5 \sqrt{2} \times \sqrt{2} } - \frac{ \sqrt{5} + 2}{10} | \times ( - 10) \\ b = | \frac{ \sqrt{5} }{10} + \frac{ \sqrt{2} }{10} - \frac{ \sqrt{5} + 2}{10} | \times ( - 10) \\ b = | \frac{ \sqrt{5} + \sqrt{2} - \sqrt{5} - 2}{10} | \times ( - 10) \\ b = | \frac{ \sqrt{2} - 2}{10} | \times ( - 10) \\ b = | \frac{ \sqrt{2} - \sqrt{4} }{10} | \times ( - 10) \\ cum \: \: \sqrt{2} < \sqrt{4} \: \: rezulta \: \: ca \: \: | \frac{ \sqrt{2} - \sqrt{4} }{10} | < 0 \: rezulta \: \: ca \: \: | \frac{ \sqrt{2} - \sqrt{4} }{10} | = - ( \frac{ \sqrt{2} - \sqrt{4} }{10} ) \\ b = - ( \frac{ \sqrt{2} - 2 }{10} ) \times ( - 10) \\ b = \frac{ - \sqrt{2} + 2}{10} \times ( - 10) \\ b = ( - \sqrt{2} + 2) \times ( - 1) \\ b = \sqrt{2} - 2[/tex]
[tex]a = \sqrt{2} + 2 \\ b = \sqrt{2} - 2 \\ mg = \sqrt{a \times b} = \sqrt{( \sqrt{2} + 2)( \sqrt{2} - 2)} = \sqrt{( \sqrt{2}) ^{2} - {2}^{2} } = \sqrt{2 - 4} = \sqrt{ - 2} [/tex]
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