Question

Calculati media geometrica a nr. reale x= 6-2 radical din 5 si y= 2 radical din 5 + 6

Answer 1

$x = 6 - 2 \sqrt{5}$

$y = 2 \sqrt{5} + 6 = 6 + 2 \sqrt{5}$

$m_{g} = \sqrt{xy}$

$m_{g} = \sqrt{(6 - 2 \sqrt{5})(6 + 2 \sqrt{5} )}$

$m_{g} = \sqrt{ {6}^{2} - {(2 \sqrt{5} )}^{2} }$

$m_{g} = \sqrt{36 - {2}^{2} \times 5}$

$m_{g} = \sqrt{36 - 4 \times 5}$

$m_{g} = \sqrt{36 - 20}$

$m_{g} = \sqrt{16}$

$m_{g} = 4$