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fizoman
@fizoman
June 2022
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[tex]2^{x+2}-2^{2-x}=15 [/tex]
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kalbim
Verified answer
4*2^(x) - 4*2^(-x) = 15
Замена:
2^(x) = t > 0
4t - 4/t = 15
(4t^2 - 4)/t = 15
15t = 4t^2 - 4
4t^2 - 15t - 4 = 0, D = 289
t1 = (15 - 17)/8 = -2/8 = -1/4 < 0 - посторонний корень
t2 = (15 + 17)/8 = 4 > 0
2^(x) = 4 = 2^2
x = 2
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Answers & Comments
Verified answer
4*2^(x) - 4*2^(-x) = 15Замена: 2^(x) = t > 0
4t - 4/t = 15
(4t^2 - 4)/t = 15
15t = 4t^2 - 4
4t^2 - 15t - 4 = 0, D = 289
t1 = (15 - 17)/8 = -2/8 = -1/4 < 0 - посторонний корень
t2 = (15 + 17)/8 = 4 > 0
2^(x) = 4 = 2^2
x = 2