Question

Media geometrica a numerelor x=(7+2 radical din 11 )(8-radical din 19) și y=(8+radical din 19 )(7-2radical din 11 )

Answer 1

$x = (7 + 2 \sqrt{11} )(8 - \sqrt{19} )$

$y = (8 + \sqrt{19} )(7 - 2 \sqrt{11} )$

$mg = \sqrt{xy}$

$mg = \sqrt{(7 + 2 \sqrt{11} )(8 - \sqrt{19} )(8 + \sqrt{19} )(7 - 2 \sqrt{11}) }$

$mg = \sqrt{( 7+2 \sqrt{11}) ( 7 - 2 \sqrt{11})(8 - \sqrt{19} )(8 + \sqrt{19)} }$

$mg = \sqrt{[ {7}^{2} - {(2 \sqrt{11} )}^{2}] \times [ {8}^{2} - {( \sqrt{19} )}^{2} ]}$

$mg = \sqrt{(49 - 44)(64 - 19)}$

$mg = \sqrt{5 \times 45}$

$mg = \sqrt{5} \times \sqrt{45}$

$mg = \sqrt{5} \times 3 \sqrt{5}$

$mg = 3 \sqrt{25}$

$mg = 3 \times 5$

$mg = 15$