Question

Resolvendo em R, a equação log(x-2)(2x² -11x+16)= 2 é
a)S = {2,3}
b)S= {2}
c)S= {-3,4}
d)S= {4}
e)S= {3}​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_{x - 2}\:(2x^2 - 11x + 16) = 2}$

$\mathsf{(x - 2)^2 = 2x^2 - 11x + 16}$

$\mathsf{x^2 - 4x + 4 = 2x^2 - 11x + 16}$

$\mathsf{x^2 - 7x + 12 = 0}$

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

$\mathsf{\Delta = (-7)^2 - 4.1.12}$

$\mathsf{\Delta = 49 - 48}$

$\mathsf{\Delta = 1}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{7 \pm \sqrt{1}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{7 + 1}{2} = \dfrac{8}{2} = 4}\\\\\mathsf{x'' = \dfrac{7 - 1}{2} = \dfrac{6}{2} = 3}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{3\}}}}\leftarrow\textsf{letra E}$