Answer
always
Work Step by Step
The equation is $x^{2}$ = $a^{2}$.
To solve the equation, we will take square root on both sides. The square root of $x^{2}$ can be $x$ or $-x$. Also, the square root of $a^{2}$ can be $a$ or $-a$. The possible equations that we would be able to derive will be $$x = a , -x = a , x = -a , -x = -a.$$ If we take the absolute value on both sides of the equation for all the above equations, we would get $|x| = |a|$ for all the scenarios as modulus eliminates the sign.
Hence, if $x^{2}$ = $a^{2}$, then $|x|$ is $\textbf{always}$ equal to $|a|$.
