Verified answer

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)

Ответ:

(2;1)

Пошаговое объяснение:

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