What is the solution of $a^2=b^2$?

Question

How to solve $a^2=b^2$?

Should I consider if the number is negative or positive?

Answer 1

$$a^2=b^2\implies a=\pm b$$ so they are either the same sign (or zero) or different sign ...

Answer 2

The equation is equivalent to $a^2-b^2 = 0$ or $(a-b)(a+b) = 0$, hence all $a,b\in\mathbb R$ with $b=a$ or $b = -a$ are solutions.

Answer 3

$$ a^2=b^2\Leftrightarrow |a|=|b| $$ $$ \Rightarrow a=b ~~~~~ \vee~~~~~ a=-b$$