Question

(unicamp) Dada a equação log x (x+6)=2, calcule o valor de x

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_x\:(x + 6) = 2}$

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

$\mathsf{x^2 - x - 6 = 0}$

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

$\mathsf{\Delta = (-1)^2 - 4.1.(-6)}$

$\mathsf{\Delta = 1 + 24}$

$\mathsf{\Delta = 25}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{1 \pm \sqrt{25}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{1 + 5}{2} = \dfrac{6}{2} = 3}\\\\\mathsf{x'' = \dfrac{1 - 5}{2} = \dfrac{-4}{2} = -2}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{3\}}}}$