Question

Calculati media geometrica a numerelor :
7 - 4radical3 si 7+4radical3

Answer 1

 

$\displaystyle\bf\\Media~geometrica~a~numerelor:\\\\7-4\sqrt{3}~~si~~7+4\sqrt{3}\\\\este:\\\\\\mg=\sqrt{\Big(7-4\sqrt{3}\Big)\Big(7+4\sqrt{3}\Big)}=\\\\~~~~~=\sqrt{7^2-\Big(4\sqrt{3}\Big)^2}=\\\\~~~~~=\sqrt{49-16\times3}=\\\\~~~~~=\sqrt{49-48}=\sqrt{1}=\boxed{\bf1}$

 

 

Answer 2

Media geometrica = $\bf \sqrt{a\cdot b}$, a,b ≥ 0

$\bf Mg= \sqrt{(7-4\sqrt{3})\cdot(7+4\sqrt{3})}$

$\bf Mg= \sqrt{(7^{2}-(4\sqrt{3})^{2}$

$\bf Mg= \sqrt{49-4^{2}\cdot 3}$

$\bf Mg= \sqrt{49-16\cdot 3}$

$\bf Mg= \sqrt{49-48}$

$\bf Mg= \sqrt{1}$

$\bf Mg= \boxed{\bf 1}$

raspuns: Mg = 1