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Aria24
@Aria24
August 2022
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Показательное уравнение:
(2^(x)+2^(-x))/(2^(x)-2^(-x))=3
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Verified answer
2^(-x) = 1 / 2^x
можно сделать замену: 2^x = a a>0
(a + (1/a)) / (a - (1/a)) = 3 a≠1
(a² + 1) / (a² - 1) = 3
a² + 1 = 3a² - 3
2a² = 4
a² = 2
a = √2 a ≠ -√2
2^x = 2^(0.5)
x = 0.5
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Answers & Comments
Verified answer
2^(-x) = 1 / 2^xможно сделать замену: 2^x = a a>0
(a + (1/a)) / (a - (1/a)) = 3 a≠1
(a² + 1) / (a² - 1) = 3
a² + 1 = 3a² - 3
2a² = 4
a² = 2
a = √2 a ≠ -√2
2^x = 2^(0.5)
x = 0.5