Let be roots of equation

MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials

Problem

Let α,β∈N\alpha, \beta \in N be roots of equation x2−70x+λ=0x^2 - 70x + \lambda = 0 , where λ2,λ3∉N\frac{\lambda}{2}, \frac{\lambda}{3} \notin N . If λ\lambda assumes the minimum possible value, then (α−1+β−1)(λ+35)∣α−β∣\frac{(\sqrt{\alpha-1} + \sqrt{\beta-1})(\lambda+35)}{|\alpha-\beta|} is equal to:

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