Question

va roggg este foarte urgent!!!​

Answer 1

 

2)

$\displaystyle\bf\\\textbf{Calculam media geometrica a numerelor reale pozitive a si b.}\\Explicatii:m_g=\sqrt{a\times b}\\\\Daca~~a<b,~atunci:~~a<m_g<b~~~si~reciproc\\\\Daca~~a = b,~atunci:~~m_g=a=b$

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$\displaystyle\bf\\Rezolvare:\\\\a)\\\\a=6\sqrt{2},~~b=3\sqrt{2}\\m_g=\sqrt{a\times b}=\sqrt{6\sqrt{2}\times 3\sqrt{2}}=\sqrt{18\Big(\sqrt{2}\Big)^2}=\sqrt{18\times2}=\sqrt{36}=6\\\\b)\\a=3\sqrt{15},~~b=5\sqrt{15}\\m_g=\sqrt{a\times b}=\sqrt{3\sqrt{15}\times5\sqrt{15}}=\sqrt{15\times15}=\sqrt{225}=15$

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$\displaystyle\bf\\c)\\a=\sqrt{3}+\sqrt{12}=\sqrt{3}+\sqrt{4\times3}=\sqrt{3}+2\sqrt{3}=3\sqrt{3}\\b=\sqrt{48}-\sqrt{3}=\sqrt{16\times3}-\sqrt{3}=4\sqrt{3}-\sqrt{3}=3\sqrt{3}\\\\a=b=3\sqrt{3}\\\\\implies~m_g=a=b=3\sqrt{3}$

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$\displaystyle\bf\\d)\\a=\sqrt{98}+\sqrt{32}-\sqrt{50}=\\\\=\sqrt{49\times2}+\sqrt{16\times2}-\sqrt{25\times2}=\\\\=7\sqrt{2}+4\sqrt{2}-5\sqrt{2}=6\sqrt{2}\\\\b=\sqrt{162}-\sqrt{72}=\sqrt{81\times2}-\sqrt{36\times2}=9\sqrt{2}-6\sqrt{2}=3\sqrt{2}\\\\m_g=\sqrt{a\times b}=\sqrt{6\sqrt{2}\times3\sqrt{2}} =\sqrt{18\times2}=\sqrt{36}=6$