Question

Responda

Log21 (x+2) + log21 (x+6) = 1

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_{21}\:(x + 2) + log_{21}\:(x + 6) = 1}$

$\mathsf{log_{21}\:(x + 2).(x + 6) = log_{21}\:21}$

$\mathsf{(x + 2).(x + 6) = 21}$

$\mathsf{x^2 + 6x + 2x + 12 = 21}$

$\mathsf{x^2 + 8x - 9 = 0}$

$\mathsf{x^2 + 8x - 9 + 25 = 0 + 25}$

$\mathsf{x^2 + 8x + 16 = 25}$

$\mathsf{(x + 4)^2 = 25}$

$\mathsf{x + 4 = \pm\:\sqrt{25}}$

$\mathsf{x + 4 = \pm\:5}}$

$\mathsf{x' = 5 - 4 = 1}}$

$\mathsf{x'' = -5 - 4 = -9}}$

$\boxed{\boxed{\mathsf{S = \{1\}}}}$