Question

calculati media geometrica a numerelor a=(√5+√3)totul la patrat si b=(√5-√3) totul la patrat.

Answer 1

[tex]a=( \sqrt{5} + \sqrt{3} )^2=\ \textgreater \ a=5+2 \sqrt{15} +3=\ \textgreater \ a=8+2 \sqrt{15} \\ b=( \sqrt{5} - \sqrt{3} )^2=\ \textgreater \ b=5-2 \sqrt{15} +3=\ \textgreater \ b=8-2 \sqrt{15} \\\\ m_g_(_a_;_b_)= \sqrt{a*b} \\m_g_(_a_;_b_)= \sqrt{(8+2 \sqrt{15} )(8- 2\sqrt{15}) } \\m_g_(_a_;_b_)= \sqrt{64-60} \\ m_g_(_a_;_b_)= \sqrt{4} \\ m_g_(_a_;_b_)=2[/tex]

****da refresh la pagina ca sa iti apara rezolvarea,e scrisa in LaTex****

Answer 2

[tex]\it m_g = \sqrt{a\cdot b} \\\;\\ a\cdot b =(\sqrt5+\sqrt3)^2(\sqrt5-\sqrt3)^2= [(\sqrt5+\sqrt3)(\sqrt5-\sqrt3)]^2 [/tex]

[tex]\it = [(\sqrt5)^2-(\sqrt3)^2]^2 = (5-3)^2 = 2^2 = 4 \\\;\\ m_g = \sqrt4 = 2[/tex]