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# a=x+y and b=x-y. If a^2=b^2, what is the value of y?

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a=x+y and b=x-y. If a^2=b^2, what is the value of y? [#permalink]  18 Jan 2013, 15:08
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$$a=x+y$$ and $$b=x-y$$. If $$a^2=b^2$$, what is the value of y?

(1) $$\sqrt{x}+\sqrt{y}>0$$

(2) $$\sqrt{x}-\sqrt{y}>0$$

M Advanced Quant, Chapter 9 (Workout Sets), Problem 73.
[Reveal] Spoiler: OA

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Re: a=x+y and b=x-y. If a^2=b^2, what is the value of y? [#permalink]  18 Jan 2013, 15:18
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$$a=x+y$$ and $$b=x-y$$. If $$a^2=b^2$$, what is the value of y?

Given that $$(x+y)^2=(x-y)^2$$ --> $$x^2+2xy+y^2=x^2-2xy+y^2$$ --> $$4xy=0$$ --> either $$x=0$$ or $$y=0$$.

(1) $$\sqrt{x}+\sqrt{y}>0$$. It's possible that $$x=0$$ and $$y$$ is any positive number, as well as, it's possible that $$y=0$$ and $$x$$ is any positive number. Not sufficient.

(2) $$\sqrt{x}-\sqrt{y}>0$$. $$x$$ cannot be 0, since in this case we'd have that $$\sqrt{y}<0$$ (which is wrong, since square root of a number is greater than or equal to 0), thus must be true that $$y=0$$. Sufficient.

Hope it's clear.
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Re: a=x+y and b=x-y. If a^2=b^2, what is the value of y? [#permalink]  23 Jun 2013, 13:19
Hello Bunuel

But square root of 4 is +/-2 correct? And -2 < 0
Can u please explain why u said square root of integer cannot b less than 0?

Posted from GMAT ToolKit
Math Expert
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a=x+y and b=x-y. If a^2=b^2, what is the value of y? [#permalink]  23 Jun 2013, 13:33
Expert's post
Shashank1149 wrote:
Hello Bunuel

But square root of 4 is +/-2 correct? And -2 < 0
Can u please explain why u said square root of integer cannot b less than 0?

Posted from GMAT ToolKit

Square root function cannot give negative result --> $$\sqrt{some \ expression}\geq{0}$$, for example $$\sqrt{x^2}\geq{0}$$ --> $$\sqrt{4}=2$$ (not +2 and -2). In contrast, the equation $$x^2=25$$ has TWO solutions, +5 and -5, because both 5^2 and (-5)^2 equal to 25.
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a=x+y and b=x-y. If a^2=b^2, what is the value of y?   [#permalink] 23 Jun 2013, 13:33
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