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Larmir
@Larmir
July 2022
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[tex]125^x+25^x=0,2^{-x} [/tex]
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nKrynka
125^x + 25^x = (0,2)^(-x)
5^(3x) + 5^(2x) - 5^(x) = 0
(5^x)*(5^2x + 5^x - 1) = 0
ОДЗ: 5^x > 0
5^x = 0 не существует
5^2x + 5^x - 1 = 0
5^x = z, z > 0
z² + z - 1 = 0
D = 1 + 4*1*1 = 5
z₁ = (-1 - √5)/2 = - (1 + √5)/2 < 0 не удовлетворяет условию z > 0
z₂ = (-1 + √5)/2
5^x = (- 1 + √5)/2
x = log₅ (- 1 + √5)/2
1 votes
Thanks 0
Larmir
Правильно ли?
Larmir
Я пришла к тому, что 5^3x+5^2x=5^x
nKrynka
Правильно Затем надо перенести (5^x) в левую часть уравнения и вынести общий множитель (5^x) за скобки.
Larmir
Спасибо
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Answers & Comments
5^(3x) + 5^(2x) - 5^(x) = 0
(5^x)*(5^2x + 5^x - 1) = 0
ОДЗ: 5^x > 0
5^x = 0 не существует
5^2x + 5^x - 1 = 0
5^x = z, z > 0
z² + z - 1 = 0
D = 1 + 4*1*1 = 5
z₁ = (-1 - √5)/2 = - (1 + √5)/2 < 0 не удовлетворяет условию z > 0
z₂ = (-1 + √5)/2
5^x = (- 1 + √5)/2
x = log₅ (- 1 + √5)/2