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karolina1978
@karolina1978
August 2022
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Решите систему уравнений с подробным объяснением
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nKrynka
Решение
(3^x) * (7^y) = 63
3^x + 7^y = 16
7^y = 16 - 3^x
(3^x) * (16 - 3^x) = 63
16*(3^x) - (3^2x) = 63
(3^2x) - 16*(3^x) + 63 = 0
3^x = t
t² - 16t + 63 = 0
t₁ = 7
t₂ = 9
1) 3^x = 7
log₃ (3^x) = log₃ 7
x * log₃ 3 = log₃ 7
x₁ = log₃ 7
2) 3^x = 9
3^x = 3²
x₂ = 2
Ответ: x₁ = log₃ 7 ; x₂ = 2
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nKrynka
7^y = 16 - 2;
7^y = 16 - 7
7^y = 9
y1 = log_7 9
7^y = 16 - 9
y 2= 7
y2 = 1
Ответ: (log₃ 7; log_7 9) ; (2; 1)
nKrynka
7^y = 7
y2 = 1
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Answers & Comments
(3^x) * (7^y) = 63
3^x + 7^y = 16
7^y = 16 - 3^x
(3^x) * (16 - 3^x) = 63
16*(3^x) - (3^2x) = 63
(3^2x) - 16*(3^x) + 63 = 0
3^x = t
t² - 16t + 63 = 0
t₁ = 7
t₂ = 9
1) 3^x = 7
log₃ (3^x) = log₃ 7
x * log₃ 3 = log₃ 7
x₁ = log₃ 7
2) 3^x = 9
3^x = 3²
x₂ = 2
Ответ: x₁ = log₃ 7 ; x₂ = 2
7^y = 16 - 7
7^y = 9
y1 = log_7 9
7^y = 16 - 9
y 2= 7
y2 = 1
Ответ: (log₃ 7; log_7 9) ; (2; 1)
y2 = 1