HMMT 2014 U16

Suppose that $x$ and $y$ are positive real numbers such that $x^{2}-x y+2 y^{2}=8$ . Find the maximum possible value of $x^{2}+x y+2 y^{2}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{72+32 \sqrt{2}}{7}

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