Let , N be roots of the equation x^2-70x+ =0, where ( )/(2),( )/(3) N.

Question

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

Answer: 60

Accepted Answer

$\begin{gathered} {x}^{2}-70x+\lambda =0 \ \alpha +\beta =70 \ \alpha \beta =\lambda \ 	herefore \alpha (70-\alpha )=\lambda \end{gathered}$

Since, 2 and 3 does not divide $\lambda $

$	herefore \alpha =5,\beta =65,\lambda =325$

By putting value of $\alpha ,\beta ,\lambda $ we get the required value $60$.

Solutions · 1