Question

Alguém sabe a resposta???​

Answer 1

Resposta:

resposta = 4

${2}^{2x + 1} - {2}^{x + 4} = {2}^{x + 2} - 32 \\ {2}^{2x} \times {2}^{1} - {2}^{x} \times {2}^{4} = {2}^{x} \times {2}^{2} - 32 \\ {2}^{x} = y \\ 2 {y}^{2} - 16y = 4y - 32 \\ 2 {y}^{2} - 16y - 4y + 32 = 0 \\ 2 {y}^{2} - 20y + 32 = 0$

calcular valores de y

∆=(-20)²-4.2.32

∆=400-256

∆=144

$y = \frac{ - ( - 20) - 12}{2 \times 2} \\ \frac{20 - 12}{4} = \frac{8}{4} = 2$

$y = \frac{ - ( - 20) + 12}{2 \times 2} \\ y = \frac{20 + 12}{4} = \frac{32}{4} = 8$

para y = 2

${2}^{x} = y \\ {2}^{x } = {2}^{1} \\ x = 1$

para y = 8

${2}^{x} = 8 \\ {2}^{x} = {2}^{3} \\ x = 3$

somando as raízes1 + 3 = 4