Quadratic Equation And Inequalities

Let \(\alpha, \beta \in \mathbf{N}\) be roots of the equation \(x^2-70 x+\lambda=0\), where \(\frac{\lambda}{2}, \frac{\lambda}{3} \notin \mathbf{N}\). If \(\lambda\) assumes the minimum possible value, then \(\frac{(\sqrt{\alpha-1}+\sqrt{\beta-1})(\lambda+35)}{|\alpha-\beta|}\) is equal to :