Question

Qual o valor de x que satisfaz a equação 2²ˣ⁺¹ - 3.2ˣ⁺²= 32

Answer 1

2^2x+1-3.2^x+2=32

(2^x)^2.2^1- 3.2^x.2^2=32
2^x=w 2w^2 -12w-32=0 ÷2 w^2-6w-16=0 ∆= 36+64 ∆=100 w= 6+/-√100/2 w'=6+10/2 w'= 16/2=8 w" = 6-10/2 w"= -4/2=-2 2^x= 8 2^x=2^3 x= 3

Answer 2

2ˣ = y

(2²ˣ).2 - 3.(2ˣ).2² = 32
y².2 - 3.y.4 = 32
2.y² - 12.y - 32 = 0
y² - 6.y - 16 = 0
Δ = 36 + 64 = 100
y' = (6 + 10)/2 = 8 V
y'' = (6 - 10)/2 = - 2 F

2ˣ = 8
2ˣ = 2³
x = 3