Question

Se considera nr nat x=4*29 si y=8*19 a) Comparati nr b) calculati media aritmetica a nr.

Answer 1

Explicație pas cu pas:

$x = {4}^{29} = {( {2}^{2} )}^{29} = {2}^{58}$

$y = {8}^{19} = {( {2}^{3} )}^{19} = {2}^{57}$

${2}^{58} > {2}^{57} \implies x > y$

$m_{a} = \frac{x + y}{2} = \frac{{2}^{58} + {2}^{57}}{2} = \frac{{2}^{57}(2 + 1)}{2} \\ = \frac{3 \cdot {2}^{57}}{2} = 3 \cdot {2}^{57 - 1} \implies m_{a} = \bf 3 \cdot {2}^{56}$