[tex]21c) \\ \text{Formula pentru calcularea mediei geometrice este urmatoarea: } \\
m_g= \sqrt{x\cdot y} \\ Rezolvare: \\
m_g= \sqrt{a \times b}= \sqrt{( \sqrt{2}-1)( \sqrt{5}+1)\times ( \sqrt{2}+1)( \sqrt{5}-1)} = \\ \\
=\sqrt{( \sqrt{2}-1)( \sqrt{2}+1)\times ( \sqrt{5}+1)( \sqrt{5}-1)} = \\ \\
=\sqrt{[( \sqrt{2})^2-(1)^2] \times [( \sqrt{5})^2-(1)^2]} = \\ \\
=\sqrt{(2-1) \times (5-1)} = \sqrt{1 \times 4}=\sqrt{4}=\boxed{2}~\Longrightarrow~Raspuns ~corect:\boxed{D}
[/tex]
