Verified answer

4√x - 3√y = 14  |*4

3√x - 4√y = 7    |*3

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x, y >= 0

и вычитаем

16√x - 12√y - 9√x + 12√y = 56 - 21

7√x = 35

√x = 5

x = 25

3*5 - 4√y = 7

4√y = 8

√y = 2

y = 4

ответ {25,4}