Question

РЕШИТЕ СИСТЕМУ УРАВНЕНИЙ
{√y+√x=7 {√xy=12
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Answer 1

{√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)