Question

O(s) valor(es) de x na equação é(são):
$log_{2}(x + 3) + log_{2}(x + 2) = 1$
me ajudem
importante!!​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_2\:(x + 3) + log_2\:(x + 2) = 1}$

$\mathsf{log_2\:(x + 3) + log_2\:(x + 2) = log_2\:2}$

$\mathsf{log_2\:(x + 3).(x + 2) = log_2\:2}$

$\mathsf{(x + 3).(x + 2) = 2}$

$\mathsf{x^2 + 2x + 3x + 6 = 2}$

$\mathsf{x^2 + 5x + 4 = 0}$

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

$\mathsf{\Delta = (5)^2 - 4.1.4}$

$\mathsf{\Delta = 25 - 16}$

$\mathsf{\Delta = 9}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{-5 \pm \sqrt{9}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{-5 + 3}{2} = -\dfrac{2}{2} = -1}\\\\\mathsf{x'' = \dfrac{-5 - 3}{2} = -\dfrac{8}{2} = -4}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{-1\}}}}$