Hard to simplify?

Algebra Level 3

If α,β\alpha,\beta are the roots of the quadratic equation

x2(3+2log233log32)x2(3log322log23)=0x^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 (α2+αβ+β2)\left( \alpha^2+\alpha\beta+\beta^2 \right) .

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