Explicație pas cu pas:
a)
[tex]a = \sqrt{3}(\sqrt{2} + 1) - \sqrt{ {(1 - \sqrt{3})}^{2} } + \sqrt{ {(1 - \sqrt{2})}^{2} } \\ = \sqrt{6} + \sqrt{3} - ( \sqrt{3} - 1) + ( \sqrt{2} - 1) \\ = \sqrt{6} + \sqrt{3} - \sqrt{3} + 1 + \sqrt{2} - 1 = \sqrt{6} + \sqrt{2}[/tex]
[tex] = > a = \sqrt{6} + \sqrt{2}[/tex]
[tex]b = \sqrt{3}(\sqrt{2} - 1) + \sqrt{ {(1 - \sqrt{3})}^{2} } - \sqrt{ {(1 - \sqrt{2})}^{2} } \\ = \sqrt{6} - \sqrt{3} + ( \sqrt{3} - 1) - ( \sqrt{2} - 1) \\ = \sqrt{6} - \sqrt{3} + \sqrt{3} - 1 - \sqrt{2} + 1 = \sqrt{6} - \sqrt{2}[/tex]
[tex] = > b = \sqrt{6} - \sqrt{2}[/tex]
b)
[tex]m_{g} = \sqrt{a \cdot b} = \sqrt{(\sqrt{6} + \sqrt{2})(\sqrt{6} - \sqrt{2})} \\ = \sqrt{6 - 2} = \sqrt{4} = 2 \\ [/tex]
[tex]= > m_{g} = 2[/tex]
