HMMT 2013 A1

Let $x$ and $y$ be real numbers with $x>y$ such that $x^{2} y^{2}+x^{2}+y^{2}+2 x y=40$ and $x y+x+y=8$ . Find the value of $x$ .

Dataset text NuminaMath olympiads. Quoted with source.

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3+\sqrt{7}

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