Question

The values of a so that the equation $\parallel x-2|-1|=a\left|x\right|$ does not contain any solution lying in the interval {2, 3} are

• A. $aϵ(-\infty \frac{1}{2})$
• B. $aϵ(1,\infty )$
• C. $aϵ(-\infty ,0)\cup (\frac{1}{2},\infty )$
• D. None of these

Answer 1

The correct option is A $aϵ(-\infty \frac{1}{2})$

The values of a so that the equation $||x-2|-1|=a\left|x\right|$ does not contains any solution lying in the interval $\{2,3\}$ are

$a\in (-\infty ,\frac{1}{2})||x-2|-1|=a\left|x\right|=>||2-2|-1|=a\left|2\right|=>|-1|=a\left|2\right|=>1=a\left|2\right|=>a=\frac{1}{2}$

Obviously, it does not contains any solution lying in the interval $\{2,3\}$ are $a\in (-\infty ,\frac{1}{2})$