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If $\alpha,\beta$ are the roots of the quadratic equation

$x^2-\left( 3+2^{\sqrt{\log_23}}-3^{\sqrt{\log_32}} \right)x-2\left( 3^{\log_32}-2^{\log_23} \right) =0$,

then find the value of $\left( \alpha^2+\alpha\beta+\beta^2 \right)$.

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