Question

Media geometrica a numerelor 8-2√15 totul sub radical si 4/√5-√3

Answer 1

    
[tex]8-2 \sqrt{15} =2(4- \sqrt{15}) \\ \frac{4}{ \sqrt{5} - \sqrt{3} } = \frac{4( \sqrt{5} + \sqrt{3})}{( \sqrt{5} - \sqrt{3})( \sqrt{5} +\sqrt{3}) }= \frac{4( \sqrt{5} + \sqrt{3})}{( \sqrt{5})^2 - (\sqrt{3})^2}= \\ \\ = \frac{4( \sqrt{5} + \sqrt{3})}{5 - 3}=\frac{4( \sqrt{5} + \sqrt{3})}{2}=2( \sqrt{5} + \sqrt{3}) \\ \\ \\ m_g = \sqrt{2(4- \sqrt{15}) \times 2( \sqrt{5} + \sqrt{3})} = \\ = \sqrt{4(4\sqrt{5} + 4\sqrt{3} - \sqrt{15}\sqrt{5} - \sqrt{15}\sqrt{3})} =[/tex]

[tex]= \sqrt{4(4\sqrt{5} + 4\sqrt{3} - 5\sqrt{3}- 3\sqrt{5})} = \\ = \sqrt{4(4\sqrt{5} - 3\sqrt{5}+ 4\sqrt{3} - 5\sqrt{3})} = \\ = \sqrt{4(\sqrt{5} - \sqrt{3})} = \boxed{2 \sqrt{\sqrt{5} - \sqrt{3}}}[/tex]