Question

Equação exponencial
2 elevado a (x²=3x-4) = 1​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{2^{(x^2 - 3x - 4)} = 1}$

$\mathsf{\not2^{(x^2 - 3x - 4)} = \not2^0}$

$\mathsf{x^2 - 3x - 4 = 0}$

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

$\mathsf{\Delta = (-3)^2 - 4.1.(-4)}$

$\mathsf{\Delta = 9 + 16}$

$\mathsf{\Delta = 25}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{3 \pm \sqrt{25}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{3 + 5}{2} = \dfrac{8}{2} = 4}\\\\\mathsf{x'' = \dfrac{3 - 5}{2} = -\dfrac{2}{2} = -1}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{4;-1\}}}}$