Verified answer

√х+√у=4

х+у-3√ху=1​

x, y >= 0

√х = a >=0

√у = b >=0

------

a + b = 4

a² + b² - 3ab = a² + 2ab + b² -2ab - 3ab = 1

-----

a + b = 4

(a + b)² - 5ab = 1

--------

a + b = 4

16 - 5ab = 1

-----

Решаем второе

5ab = 15

-------

ab = 3

a = 4 - b

---------

второе в первое и до конца решаем

(4 - b)b = 3

b² - 4b + 3 = 0

D = 16 - 12 = 4

b₁₂ = (4 +- 2)/2 = 1   3

1.b₁ = 1

√y = 1    y = 1

a₁ = 4 - b₁ = 3

√x = 3   x = 9

2.b₂ = 3

√y = 3    y = 9

a₂ = 4 - b₂ = 1

√x = 1   x = 1

ответ (1, 9) (9,1)