Question

Azi am dat teza la mate si trebuia a aflam media geometrica numerelor a si b
$a = \sqrt{6} + \frac{12}{ \sqrt{6} }$
$b = \sqrt{54} - \sqrt{6}$
imi puteti spune media geometrica ?
dau COROANĂ​

Answer 1

Explicație pas cu pas:

Media geometrica

$\sqrt{a \times b}$

$\sqrt{6} + \frac{12}{ \sqrt{6} } = \frac{6 + 12}{ \sqrt{6} } = \frac{18}{ \sqrt{6} } \\ \sqrt{54} - \sqrt{6} = \sqrt{9 \times 6} - \sqrt{6} = \\ 3 \sqrt{6} - \sqrt{6} = 2 \sqrt{6}$

$\sqrt{a \times b} = \sqrt{ \frac{18}{ \sqrt{6} } \times 2 \sqrt{6} } = \sqrt{36} = 6$