Question

calculati media aritmetica a numerelor : x=(
$x = ( \sqrt{3} - 1) {}^{2} + 2 \sqrt{3 \: } \\ y = ( \sqrt{5} - 2) \times ( \sqrt{5} + 2) + 2016 \: la \: puterea \: 0$

Answer 1

$x = {( \sqrt{3} - 1) }^{2} + 2 \sqrt{3}$

$x = 3 - 2 \sqrt{3} + 1 + 2 \sqrt{3}$

$x = 4$

$y = ( \sqrt{5} - 2)( \sqrt{5} + 2) + {2016}^{0}$

$y = 5 - 4 + 1$

$y = 2$

$m_{a} = \frac{x + y}{2}$

$m_{a} = \frac{4 + 2}{2}$

$m_{a} = \frac{6}{2}$

$m_{a} = 3$

Answer 2

Aplicam formulele : 
( x - y )² = x² - 2xy + y²
( x - y )( x + y ) = x² - y²
---------------------------
x = (√3)² - 2·√3·1+1² + 2√3 = 3 - 2√3 + 1 + 2√3 = 4
y = (√5)² - 2² + 1 = 5 - 4 + 1 = 2

media aritmetica : ( x + y ) / 2 = ( 4 + 2 ) / 2 = 6 / 2 = 3