Question

*Me ajudeeeem , urgenteeeee*
Resolva a equação exponencial abaixo e assinale a solução correta: 2²×-9•2×+8=0
A) S= {0,5}
B) S= {0,3}
C) S= {1,6}
D) S= {2,6} ​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{2^{2x} - 9.2^x + 8 = 0}$

$\mathsf{y = 2^x}$

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

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

$\mathsf{\Delta = (-9)^2 - 4.1.8}$

$\mathsf{\Delta = 81 - 32}$

$\mathsf{\Delta = 49}$

$\mathsf{y = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{9 \pm \sqrt{49}}{2} \rightarrow \begin{cases}\mathsf{y' = \dfrac{9 + 7}{2} = \dfrac{16}{2} = 8}\\\\\mathsf{y'' = \dfrac{9 - 7}{2} = \dfrac{2}{2} = 1}\end{cases}}$

$\mathsf{2^x = 8}$

$\mathsf{\not2^x = \not2^3}$

$\mathsf{x = 3}$

$\mathsf{2^x = 1}$

$\mathsf{\not2^x = \not2^0}$

$\mathsf{x = 0}$

$\boxed{\boxed{\mathsf{S = \{0;3\}}}}\leftarrow\textsf{letra B}$