Question

How many roots does the following equation possess $3^{|x|}\left\{|2-|x||\right\}=1?$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (D)

$4$

Here, $3^{|x|}\left\{|2-|x||\right\}=1$ $\Rightarrow |2-|x||=3^{-|x|}$
In order to determine the number of roots, it is sufficient to find the points of intersection of the curves $y=|2-|x||$ and $y=3^{-|x|}$, shown in the graph;
We observe the two curves intersect at four points.
$\therefore$ Four real solutions exist.
Hence, $\left(D\right)$ is the correct answer.