Răspuns:
[tex]x + y = 2 \sqrt{3} \\ {x}^{2} - {y}^{2} = 4 \sqrt{6} \\ {x }^{2} - {y}^{2} = (x + y)(x - y) \\ 4 \sqrt{6} = 2 \sqrt{3} (x - y) \\ x - y = \frac{4 \sqrt{6} }{2 \sqrt{3} } \\ x - y = 2 \sqrt{2} \\ facem \: um \: sistem \: dim cele \: doua \\ x + y = 2 \sqrt{3} \\ x - y = 2 \sqrt{2} \\ 2x = 2 \sqrt{3} - 2 \sqrt{2} \\ x = \frac{2( \sqrt{3} - \sqrt{2} )}{2} \\ x = \sqrt{3} - \sqrt{2 } \\ x + y = 2 \sqrt{3} \\ \sqrt{3} - \sqrt{2} + y = 2 \sqrt{3} \\ y = 2 \sqrt{3} - \sqrt{3} + \sqrt{2} \\ y = \sqrt{3 } + \sqrt{2} \\ mg = \sqrt{x \times y } \\ = \sqrt{( \sqrt{3} - \sqrt{2})( \sqrt{3} + \sqrt{2} ) } \\ = \sqrt{3 + \sqrt{6} - \sqrt{6} - 2 } \\ \sqrt{3 - 2} \\ \sqrt{1} = 1 \\ \\ mg = 1[/tex]
