Question

1.Aflati media geometrica a numerelor a si b daca:
A)2 radical din 5 si b=10 radical din 5
B)a=6 radical din 3 si b=8 radical din 3
C)a=2 radical din 5 -radical din 14 si b=8 radical din 5-4 radical din 14
d)a=18 supra 5 si b= 1 supra 10
Ajutor va rog!!!

Answer 1

[tex]a)M_g=\sqrt{2\sqrt{5}\cdot10\sqrt{5}}=\sqrt{20\cdot 5}=10 \\ b)M_g=\sqrt{6\sqrt{3}\cdot 8 \sqrt{3}}=\sqrt{48 \cdot 3}=12\\ c)M_g=\sqrt{(2\sqrt{5}-\sqrt{14})\cdot(8\sqrt{5}-4\sqrt{14})}=\\ =\sqrt{(2\sqrt{5}-\sqrt{14})\cdot4(2\sqrt{5}-\sqrt{14})}=\\ =\sqrt{[(2\sqrt{5})^2-(\sqrt{14})^2]\cdot4}=\\ =\sqrt{(20-14)\cdot4}=\\ =2\sqrt{6}\\ d)M_g= \sqrt{ \frac{18}{5}\cdot \frac{1}{10} } = \sqrt{\frac{18}{50}} =\sqrt{ \frac{9}{25} }= \frac{3}{5} [/tex]