What should be added to $x^{2} + x y + y^{2}$ to obtain $2 x^{2} + 3 x y$

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Solution

Let $λ$ will be added

$∴ x^{2} + x y + y^{2} + λ = 2 x^{2} + 3 x y$

$\Rightarrow λ = x^{2} + 2 x y - y^{2}$

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