What instance that this equation would be true?
$|x+y|=|x|+|y|$ Given that $x$, $y$ are elements of real numbers.
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1It is true whenever $xy\ge 0$. – Mark Viola Jul 07 '15 at 05:47
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$x$ and $y$ are of the same parity. – Bumblebee Jul 07 '15 at 08:01
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This seems to be a duplicate of http://math.stackexchange.com/questions/944302/when-does-the-equality-hold-in-the-triangle-inequality or http://math.stackexchange.com/questions/226569/equality-holds-in-triangle-inequality-iff-both-numbers-are-positive-both-are-ne (You can probably find a few more related posts.) – Martin Sleziak Jul 07 '15 at 08:08
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I guess you are asking in connection with your previous questions. – Martin Sleziak Jul 07 '15 at 08:11
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$|x+y|=|x|+|y| \iff |x+y|^2 = (|x|+|y|)^2 \iff x^2+2xy+y^2=x^2+2|xy|+y^2 \iff xy=|xy| \iff xy \geq 0$.
DeepSea
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The statement will be true when any of the following conditions is satisfied:
(i) $x=0$ or $y=0$ or both are zero,
(ii) $x=y$,
(iii) $x\ge0$ and $y\ge0$,
(iv) $x\le0$ and $y\le0$.
K. Nantomah
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