# Linear Transformation

Algebra Level 4

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

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

Find $$p+q$$.

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