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When is x+y=the square root of x squared is y squared true and when is it false? Please solve this using basic algebra. Thank you.

 Apr 3, 2016
 #1
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it's always true

 

\(x+y = \sqrt{{(x+y)}^{2}}\)

you square X+Y then immediately square root it.

the square root cancels out the original square.

 Apr 3, 2016
 #2
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When is x+y=the square root of x squared is y squared true and when is it false? Please solve this using basic algebra. Thank you.

 

\(x+y=\sqrt{x^2}\\ x+y=|x|\\ If\; x\;\ge0\; then\; y=0\\~\\ If\; x\; <0 \;then\\ x+y=-x\\ y=-2x\\\)

 

So no y is not often a squared number although it can be sometimes.

 Apr 3, 2016

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