Quick Algebra Identities

Algebra Level 2

\[\large \color{red}{x} = \color{green} {\dfrac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} }}, \quad \quad \color{purple}{y} = \color{orange}{\dfrac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} }}, \quad\quad \color{magenta}{x^2 + xy + y^2} = \, ? \]

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