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If x^2 = y^2 which of the following must be true?
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Updated on: 08 Oct 2022, 05:42
Updated on: 08 Oct 2022, 05:42
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Question Stats:
99% (00:48) correct
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If \(x^2 = y^2\) which of the following must be true?
Indicate all that apply
1. \(x=y\)
2.\( x^2 - y^2 = 0\)
3. \(|x| - |y| = 0\)
Indicate all that apply
1. \(x=y\)
2.\( x^2 - y^2 = 0\)
3. \(|x| - |y| = 0\)
Originally posted by manvijain08 on 08 Oct 2022, 03:02.
Last edited by Carcass on 08 Oct 2022, 05:42, edited 3 times in total.
Last edited by Carcass on 08 Oct 2022, 05:42, edited 3 times in total.
Updated
If x^2 = y^2 which of the following must be true?
[#permalink]
08 Oct 2022, 05:40
08 Oct 2022, 05:40
1
Expert Reply
B is \(x^2-y^2=0\) or \(x^2=y^2\) so statement B is correct
C is \(|x|-|y|= 0\) or \(|x|=|y|\) so the absolute value means that always x=y Both must be positive. So C is also true
A x=y this NOT always is true when we have to deal with \(x^2\) and \(y^2\) because even power can hide the underneath sign of the values
IF \(x=-1\) and \(y=1\) then \(x^2=y^2\) is valid because \(-1^2=1^2 >>> 1=1\)
IF \( x=1\) and \(y=1\) then \(x^2=y^2\) is valid because \(1^2=1^2 >>> 1=1\)
So could we have \(x=y\) but also \(x \neq y\)
Therefore A is NOT true
B and C are our answers
C is \(|x|-|y|= 0\) or \(|x|=|y|\) so the absolute value means that always x=y Both must be positive. So C is also true
A x=y this NOT always is true when we have to deal with \(x^2\) and \(y^2\) because even power can hide the underneath sign of the values
IF \(x=-1\) and \(y=1\) then \(x^2=y^2\) is valid because \(-1^2=1^2 >>> 1=1\)
IF \( x=1\) and \(y=1\) then \(x^2=y^2\) is valid because \(1^2=1^2 >>> 1=1\)
So could we have \(x=y\) but also \(x \neq y\)
Therefore A is NOT true
B and C are our answers
gmatclubot
If x^2 = y^2 which of the following must be true? [#permalink]
08 Oct 2022, 05:40
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