Question

2^2019+2^2020+2^2021/x=32^404/0,5
X diferit de 0​

Answer 1

Răspuns:

Explicație pas cu pas:

2^2019+2^2020+2^2021 = 2^2019*(1 + 2 + 2^2) = 7*2^2019

32^404 = (2^5)^404 = 2^2020

0,5 = 5/10 = 1/2

2^2020/(1/2) = 2^2020*2/1 = 2^2021

7*2^2019/x = 2^2021

x = 7*2^2019/2^2021 = 7/2^2 = 7/4

Answer 2

Răspuns:

$x = \frac{7}{4}$

Explicație pas cu pas:

$\frac{ {2}^{2019} + {2}^{2020} + {2}^{2021} }{x} = \frac{ {32}^{404} }{0,5} \: , \: x \neq 0$

$\frac{2 {}^{2019}(1 + 2 + {2}^{2} )}{x} = \frac{(2 {}^{5} ) {}^{404} }{ \frac{1}{2} }$

$\frac{ {2}^{2019}(1 + 2 + 4) }{x} = 2^{2020} \cdot 2$

$\frac{ {2}^{2019} \cdot7}{x} = {2}^{2021}$

${2}^{2019} \cdot 7 = {2}^{2021} \cdot x$

${2}^{2021} \cdot x = 7 \cdot {2}^{2019}$

$x = \frac{7 \cdot {2}^{2019} }{ {2}^{2021} } = \frac{7}{ {2}^{2} } = \boxed{ \frac{7}{4}}$