[tex]\it x^2=a^2 \Leftrightarrow \sqrt{x^2} =\sqrt{a^2} \ \ \ (1)
\\\;\\
a \geq0 \ \ \ \ (2)
\\\;\\
(1), (2) \Longrightarrow |x| =a \Longrightarrow x = \pm a[/tex]
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[tex]\it x^2=-a^2 \Leftrightarrow x^2=i^2a^2 \Leftrightarrow \sqrt{x^2} =\sqrt{i^2a^2} \ \ \ (1) \\\;\\ a \geq0 \ \ \ \ (2) \\\;\\ (1), (2) \Longrightarrow |x| =ai \Longrightarrow x = \pm ai [/tex]
