Question

Am incercat si eu sa rezolv
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Answer 1

$a = 3+\sqrt{5}\\\\b = 3 - \sqrt{5}\\\\ m_a = \frac{a+b}{2} = \frac{3+\sqrt{5} + 3 - \sqrt{5}}{2} = \frac{6}{2} = 3\\\\ m_g = \sqrt{ab} = \sqrt{(3+\sqrt{5})(3 - \sqrt{5})} = \sqrt{3^2 - {(\sqrt{5})}^2} = \sqrt{9 - 5} = \sqrt{4} = 2 \\\\ m_a - m_g = 3 - 2\implies \boxed{m_a - m_g = 1}$