Question

A solução para a equação abaixo é: * (log₂ x)² - log₂x = 2
S = {4; 1/2}
S = {2; 1/4}
S = {2; 1/2}
S = {4; 1/4}
S = {2; -1}​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{(log_2\:x)^2 -log_2\:x = 2 }$

$\mathsf{(log_2\:x)^2 -log_2\:x - 2 = 0}$

$\mathsf{y = log_2\:x}$

$\mathsf{y^2 - y - 2 = 0}$

$\mathsf{\Delta = b^2 - 4.a.c}$

$\mathsf{\Delta = (-1)^2 - 4.1.(-2)}$

$\mathsf{\Delta = 1 + 8}$

$\mathsf{\Delta = 9}$

$\mathsf{y = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{1 \pm \sqrt{9}}{2} \rightarrow \begin{cases}\mathsf{y' = \dfrac{1 + 3}{2} = \dfrac{4}{2} = 2}\\\\\mathsf{y'' = \dfrac{1 - 3}{2} = \dfrac{-2}{2} = -1}\end{cases}}$

$\mathsf{log_2\:x = 2}$

$\mathsf{x = 2^2 = 4}$

$\mathsf{log_2\:x = -1}$

$\mathsf{x = 2^{-1} = \dfrac{1}{2}}$

$\boxed{\boxed{\mathsf{S = \left\{4;\dfrac{1}{2}\right\}}}}\leftarrow\textsf{letra A}$