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annaelchinova
@annaelchinova
August 2022
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ОООчень нужно 14*4^x-9*2^x+1=0
промежуток [-4;-2].
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nKrynka
Решение
14*4^x - 9*2^x + 1 = 0
14*2^(2x) - 9*(2^x) + 1 = 0
2^x = t
14t² - 9t + 1 = 0
D = 81 - 4*14*1 = 25
t₁ = (9 - 5)/28
t₁ = 1/7
t₂ = (9 + 5)/28
t₂ = 1/2
1) 2^x = 1/7
log₂ 2^x = log₂ (1/7)
x₁ = log₂ (1/7)
2) 2^x = 1/2
2^x = 2⁻¹
x = - 1
2 votes
Thanks 4
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Answers & Comments
14*4^x - 9*2^x + 1 = 0
14*2^(2x) - 9*(2^x) + 1 = 0
2^x = t
14t² - 9t + 1 = 0
D = 81 - 4*14*1 = 25
t₁ = (9 - 5)/28
t₁ = 1/7
t₂ = (9 + 5)/28
t₂ = 1/2
1) 2^x = 1/7
log₂ 2^x = log₂ (1/7)
x₁ = log₂ (1/7)
2) 2^x = 1/2
2^x = 2⁻¹
x = - 1