UK | A Nice Algebra Problem | Math Olympiad

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Find the value of x and y?
How to solve √x + y = 7 and x + √y = 11

In this video, we'll show you How to Solve Math Olympiad Question A Nice Algebra Problem √x + y = 7 and x + √y = 11 in a clear , fast and easy way. Whether you are a student learning basics or a professtional looking to improve your skills, this video is for you. By the end of this video, you'll have a solid understanding of how to solve math olympiad exponential equations and be able to apply these skills to a variety of problems.
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[YAWTon]

x=9, y=4 is an obvious solution. Where is the proof that it is the only solution? Did you forget to specify that x and y are required to be integers?
If x and y are required to be integers, then x and y must be perfect squares, otherwise their square roots would be irrational, and so would be the right hand sides of the two equations. Therefore y must be a square <7, i.e. y=1 or y=4. If y=1 then √x=10, x=100, but x <10 from the second equation. Therefore y=4, and x=11-√4=9 from the second equation.

[SGuerra]

É necessário deixar claro que os valores de x e y são inteiros. Sem essa informação é possível chegar em uma equação de grau 4 para ter uma resposta definitiva.