# Sum Reciprocal Two

Algebra Level 5

$$\alpha, \beta > 0$$.

With $$\alpha, \beta > 0$$, if $$\alpha + \dfrac{1}{\alpha}$$ and $$2 - \beta - \dfrac{1}{\beta}$$ are the roots of the quadratic equation

$x^{2} -2(a+1)x + a - 3 = 0,$

then find the sum of integral values of $$a$$.

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