Question

log 3 * (x - 1) ^ 2 = 2​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\sf log\:3\:.\:(x - 1)^2 = 2$

$\sf log\:3\:.\:(x^2 - 2x + 1) = log 10^2$

$\sf log\:(3x^2 - 6x + 3) = log\:100$

$\sf 3x^2 - 6x + 3 = 100$

$\sf 3x^2 - 6x - 97 = 0$

$\sf a = 3 \Leftrightarrow b = -6 \Leftrightarrow c = -97$

$\sf \Delta = b^2 - 4.a.c$

$\sf \Delta = (-6)^2 - 4.3.(-97)$

$\sf \Delta = 36 + 1.164$

$\sf \Delta = 1.200$

$\sf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{6 \pm \sqrt{1.200}}{6} \rightarrow \begin{cases}\sf{x' = \dfrac{6 + 20\sqrt{3}}{6} = \dfrac{3 + 10\sqrt{3}}{3}}\\\\\sf{x'' = \dfrac{6 - 20\sqrt{3}}{6} = \dfrac{3 - 10\sqrt{3}}{3}}\end{cases}}$

$\boxed{\boxed{\sf S = \left\{\dfrac{3 + 10\sqrt{3}}{3}\:,\dfrac{3 - 10\sqrt{3}}{3}\right\}}}$