Linear Transformation

Algebra Level 4

Let α\alpha and β\beta be the roots of the equation x22x2=0x^2-2x-2=0 such that α<β\alpha<\beta.

The value of the α2β\alpha-2\beta can be expressed as pq3-p-q\sqrt{3}, where pp and qq are positive integers.

Find p+qp+q.

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