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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