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Let α\alphaα and β\betaβ be the roots of the equation x2−2x−2=0x^2-2x-2=0x2−2x−2=0 such that α<β\alpha<\betaα<β.
The value of the α−2β\alpha-2\betaα−2β can be expressed as −p−q3-p-q\sqrt{3}−p−q3, where ppp and qqq are positive integers.
Find p+qp+qp+q.
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