HMMT 2024 U22

Let $x<y$ be positive real numbers such that

$\sqrt{x}+\sqrt{y}=4 \text { and } \sqrt{x+2}+\sqrt{y+2}=5$

Compute $x$ .

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

\frac{49}{36}

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