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If (x − y)^2 = x^2 + y^2 , then which one of the following statements

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If (x − y)^2 = x^2 + y^2 , then which one of the following statements  [#permalink]

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New post Updated on: 08 Jul 2019, 00:24
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A
B
C
D
E

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Question Stats:

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Originally posted by Bunuel on 01 Jun 2017, 11:08.
Last edited by SajjadAhmad on 08 Jul 2019, 00:24, edited 1 time in total.
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Re: If (x − y)^2 = x^2 + y^2 , then which one of the following statements  [#permalink]

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New post 01 Jun 2017, 11:57
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Bunuel wrote:
If \((x − y)^2 = x^2 + y^2\), then which one of the following statements must also be true?

I. x = 0
II. y = 0
III. xy = 0

(A) None
(B) I only
(C) II only
(D) III only
(E) II and III only


Given: (x − y)² = x² + y²
Expand the left side to get: x² - xy - xy + y² = x² + y²
Simplify the left side to get: x² - 2xy + y² = x² + y²
Subtract x² from both sides: -2xy + y² = y²
Subtract y² from both sides: -2xy = 0
Divide both sides by -2 to get: xy = 0

So, III is true.
However, just because xy = 0, we can't say for sure whether x = 0 or y = 0.
All we know is that at least one of those variables equals 0.

Answer:

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Re: If (x − y)^2 = x^2 + y^2 , then which one of the following statements   [#permalink] 01 Jun 2017, 11:57
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If (x − y)^2 = x^2 + y^2 , then which one of the following statements

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