Sum Reciprocal Two

Algebra Level 5

α,β>0 \alpha, \beta > 0 .

With α,β>0 \alpha, \beta > 0 , if α+1α \alpha + \dfrac{1}{\alpha} and 2β1β 2 - \beta - \dfrac{1}{\beta} are the roots of the quadratic equation

x22(a+1)x+a3=0,x^{2} -2(a+1)x + a - 3 = 0,

then find the sum of integral values of aa.

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