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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] New post 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] New post 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.

Answer: B.

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] New post 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?

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a=x+y and b=x-y. If a^2=b^2, what is the value of y? [#permalink] New post 23 Jun 2013, 13:33
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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?

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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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