Show that $|a+b|=|a|+|b|$ iff $a b \geq 0$
Added by Francisco G.
Step 1
Assume that $|a+b|=|a|+|b|$. We know that $|x|\geq 0$ for any real number $x$. Therefore, $|a+b|\geq 0$ and $|a|+|b|\geq 0$. Now, we can square both sides of the equation $|a+b|=|a|+|b|$ to get rid of the absolute values: $$(|a+b|)^2=(|a|+|b|)^2$$ Expanding Show more…
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