{√y+√x=7
{√xy=12
x, y > 0
√x = a > 0
√y = b
a + b = 7
ab = 12
a = 7 - b
(7 - b)b = 12
7b - b² = 12
b² - 7b + 12 = 0
D = 49 - 4*12 = 1
b₁₂ = (7 ± 1)/2 = 3 4
1. b = 3
√y = 3
y = 9
a = 7 - b = 7 - 3 = 4
√x = 4
x = 16
2. b = 4
√y = 4
y = 16
a = 7 - b = 7 - 4 = 3
√x = 3
x = 9
ответ (9, 16) (16, 9)
{√y+√x=7
{√xy=12
x, y > 0
√x = a > 0
√y = b
a + b = 7
ab = 12
a = 7 - b
(7 - b)b = 12
7b - b² = 12
b² - 7b + 12 = 0
D = 49 - 4*12 = 1
b₁₂ = (7 ± 1)/2 = 3 4
1. b = 3
√y = 3
y = 9
a = 7 - b = 7 - 3 = 4
√x = 4
x = 16
2. b = 4
√y = 4
y = 16
a = 7 - b = 7 - 4 = 3
√x = 3
x = 9
ответ (9, 16) (16, 9)