Explicație pas cu pas:
[tex]x = \frac{5}{ \sqrt{7} - \sqrt{2} } + \frac{2}{3 + \sqrt{7} } = \\ = \frac{5(\sqrt{7} + \sqrt{2})}{( \sqrt{7} - \sqrt{2})(\sqrt{7} + \sqrt{2}) } + \frac{2(3 - \sqrt{7})}{ (3 + \sqrt{7})(3 - \sqrt{7}) } \\ = \frac{5(\sqrt{7} + \sqrt{2})}{7 - 2} + \frac{2(3 - \sqrt{7})}{9 - 7} \\ = \frac{5(\sqrt{7} + \sqrt{2})}{5} + \frac{2(3 - \sqrt{7})}{2} = \sqrt{7} + \sqrt{2} + 3 - \sqrt{7} \\ = > x = 3 + \sqrt{2} [/tex]
[tex]3 > \sqrt{2} = > y = \sqrt{ {(3 - \sqrt{2} )}^{2} } = 3 - \sqrt{2} \\ [/tex]
[tex]m_{a} = \frac{x + y}{2} = \frac{3 + \sqrt{2} + 3 - \sqrt{2} }{2} = \frac{6}{2} \\ = > m_{a} = 3[/tex]
[tex]m_{g} = \sqrt{xy} = \sqrt{(3 + \sqrt{2})(3 - \sqrt{2})} = \sqrt{9 - 2} \\ = > m_{g} = \sqrt{7}[/tex]
