Question

Resolva a inequação
㏒3(-x² + 10x) ≤ 2

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\sf{log_3\:(-x^2 + 10x) \leq 2}$

$\sf{log_3\:(-x^2 + 10x) \leq log_3\:3^2}$

$\sf{log_3\:(-x^2 + 10x) \leq log_3\:9}$

$\sf{-x^2 + 10x \leq 9}$

$\sf{x^2 - 10x + 9 \geq 0}$

$\sf{x^2 - 10x + 9 + 16 \geq 0 + 16}$

$\sf{x^2 - 10x + 25 \geq 16}$

$\sf{(x - 5)^2 \geq 16}$

$\sf{x - 5 \geq \pm\:\sqrt{16}}$

$\sf{x - 5 \geq \pm\:4}$

$\sf{x' \geq 4 + 5 \geq 9}$

$\sf{x'' \geq -4 + 5 \geq 1}$

$\boxed{\boxed{\sf{S = \{\:]\:0\:,\:1\:]\cup \:[\:9\:,\:10\:[\:\}}}}$