Quick Algebra Identities

Algebra Level 2

x=323+2,y=3+232,x2+xy+y2=?\large \color{#D61F06}{x} = \color{#20A900} {\dfrac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} }}, \quad \quad \color{#69047E}{y} = \color{#EC7300}{\dfrac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} }}, \quad\quad \color{magenta}{x^2 + xy + y^2} = \, ?

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