Question

Resolva em R, a equação ℓog (x – 3) (3x + 1) = 1​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\mathsf{log\:(x - 3).(3x + 1) = 1}$

$\mathsf{log\:(x - 3).(3x + 1) = log\:10}$

$\mathsf{(x - 3).(3x + 1) = 10}$

$\mathsf{3x^2 + x - 9x - 3 - 10 = 0}$

$\mathsf{3x^2 - 8x - 13 = 0}$

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

$\mathsf{\Delta = (-8)^2 - 4.(3).(-13)}$

$\mathsf{\Delta = 64 + 156}$

$\mathsf{\Delta = 220}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{8 \pm \sqrt{220}}{6} \rightarrow \begin{cases}\mathsf{x' = \dfrac{8 + 2\sqrt{55}}{6} = \dfrac{4 + \sqrt{55}}{3}}\\\\\mathsf{x'' = \dfrac{8 - 2\sqrt{55}}{6} = \dfrac{4 - \sqrt{55}}{3}}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{\:\dfrac{4 + \sqrt{55}}{3}\:;\:\dfrac{4 - \sqrt{55}}{3}\:\}}}}$