Question

The number of roots of $3^{\left|x\right|·\left|2-\left|x\right|\right|}=1$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C

$3$

Explanation for correct option

Given equation is,

$$\begin{gathered} 3^{\left|x\right|·\left|2-\left|x\right|\right|}=1 \\ \Rightarrow 3^{\left|x\right|·\left|2-\left|x\right|\right|}=3^0 \\ \therefore \left|x\right|·\left|2-\left|x\right|\right|=0 \end{gathered}$$

Either $\left|x\right|=0$ or $\left|x\right|=2$

$\therefore x=0$ or $x=\pm 2$

Therefore the number of roots is $=3$

Hence, the correct option is $\left(\mathrm{C}\right)$