Question

resolver 3^x-3^4-x=24

Answer 1

Resposta:

x 4 - x

3 - 3 = 24

x 4

3 - 3

--------- = 24

x

3

x

3 = y

y - 81 24

----- =

y

y² - 81 = 24y

--------- ------

y y

y² - 81 = 24y

y² - 24y - 81 = 0

a = 1; b = - 24; c = - 81

Δ = b² - 4ac

Δ = (-24)² - 4.1.(-81)

Δ = 576 + 324

Δ = 900

a = 1; b = - 24; c = - 81

y = - b +/- √Δ - (-24) +/- √900

-------------- = ------------------------

2a 2.1

y' = 24 + 30 54

----------- = -------- = 27

2 2

y" = 24 - 30 - 6

----------- = ------- = - 3

2 2

y = - 3

x

3 = y

x

3 = - 3 (impossível)

y = 27

x

3 = y

x

3 = 27

x 3

3 = 3

x = 3

R.: x = 3