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

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

Should I consider if the number is negative or positive?

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3 Answers

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

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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.

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

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