Let α, β ∈ N be roots of the equation x^2-70 x+λ=0, where (λ)/2, (λ)/3 ∉ N. If λ assumes the minimum possible value, then…

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