log(3)(x + y) + log(3)(x - y) = 1
одз x > y
x > -y
x,y > 0
4^(x/y + y/x) = 32
(2^2)^(x/y + y/x) = 2^5
2(x/y + y/x) = 5
x/y = t
2t + 2/t - 5 = 0
2t² - 5t + 2 = 0
D = 25 - 16 = 9
t12 = (5 +- 3)/4 = 2 1/2
1. t = 1/2
x/y = 1/2
2x = y
2. t = 2
x/y = 2
x = 2y
log(3)(x - y)(x + y) = log(3) 3
x² - y² = 3
1. x = 2y
4y² - y² = 3
3y² = 3
y² = 1
y = -1 нет
y = 1 x = 2
2. x = 2y x > y нет (x² - 4x² = 3 -3x² = 3 нет)
ответ (2,1)
(2;1)
Пошаговое объяснение:
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log(3)(x + y) + log(3)(x - y) = 1
одз x > y
x > -y
x,y > 0
4^(x/y + y/x) = 32
(2^2)^(x/y + y/x) = 2^5
2(x/y + y/x) = 5
x/y = t
2t + 2/t - 5 = 0
2t² - 5t + 2 = 0
D = 25 - 16 = 9
t12 = (5 +- 3)/4 = 2 1/2
1. t = 1/2
x/y = 1/2
2x = y
2. t = 2
x/y = 2
x = 2y
log(3)(x + y) + log(3)(x - y) = 1
log(3)(x - y)(x + y) = log(3) 3
x² - y² = 3
1. x = 2y
4y² - y² = 3
3y² = 3
y² = 1
y = -1 нет
y = 1 x = 2
2. x = 2y x > y нет (x² - 4x² = 3 -3x² = 3 нет)
ответ (2,1)
(2;1)
Пошаговое объяснение:
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