Let , N be roots of equation x^2-70 x+ =0, where 2 , 3 N. If assu… - Vidyadip

MCQ

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

A
$88$
B
$80$
C
$70$
✓
$60$

✓

Answer

Correct option: D.

$60$

d
$ x^2-70 x+\lambda=0 $

$ \alpha+\beta=70 $

$ \alpha \beta=\lambda $

$ \therefore \alpha(70-\alpha)=\lambda$

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

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

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

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