Question

Resolva a seguinte equação : 2/x + 1/(x-2) + 2/(x+2) = 1/(x² - 4

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{\dfrac{2}{x} + \dfrac{1}{(x - 2)} + \dfrac{2}{(x + 2)} = \dfrac{1}{(x^2 -4)}}}}$

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

$\mathsf{(2x^2 - 8) + (x^2 + 2x) + (2x^2 - 4x) = x}$

$\mathsf{5x^2 - 3x - 8 = 0}$

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

$\mathsf{\Delta = (-3)^2 - 4.5.(-8)}$

$\mathsf{\Delta = 9 + 160}$

$\mathsf{\Delta = 169}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{3 \pm \sqrt{169}}{10} \rightarrow \begin{cases}\mathsf{x' = \dfrac{3 + 13}{10} = \dfrac{16}{10} = \dfrac{8}{5}}\\\\\mathsf{x'' = \dfrac{3 - 13}{10} = \dfrac{-10}{10} = -1}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{\dfrac{8}{5}; -1\}}}}$