Jee Main Jan 30 Shift 1 Mathematics - Question10
Question 10
Given $x^{2}-70 x+\lambda=0$ with positive roots $\alpha$ and $\beta$ where one of the root is less than 10 and $\frac{\lambda}{2}$ and $\frac{\lambda}{3}$ are not integers then find value of $\frac{\sqrt{\alpha-1}+\sqrt{\beta-1}}{|\alpha-\beta|}$ is equal to
(1) $\frac{1}{5}$
(2) $\frac{1}{12}$
(3) $\frac{1}{60}$
(4) $\frac{1}{70}$
Show Answer
Answer: (1)
Solution:
Given : $x^{2}-70 x+\lambda=0$
$\Rightarrow$ Let roots be $\alpha$ and $\beta$
$\Rightarrow \beta=70-\alpha$
$\lambda=\alpha(70-\alpha)$
$\lambda$ is not divisible by 2 and 3
$\Rightarrow \alpha=5, \beta=65$
$\Rightarrow \frac{\sqrt{5-1}+\sqrt{65-1}}{|60|}=\left|\frac{4+8}{60}\right|=\frac{1}{5}$
BETA
