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If x^2=y^2, which of the following must be true?
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22 Jul 2025, 00:57
22 Jul 2025, 00:57
Expert Reply
00:00
Question Stats:
60% (00:43) correct
39% (00:35) wrong based on 33 sessions
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If \(x^2=y^2\), which of the following must be true?
Select all that apply.
❏ \(|x|-|y|=0\)
❏ \(\frac{x}{y}=1\)
❏ \(x=y\)
Select all that apply.
❏ \(|x|-|y|=0\)
❏ \(\frac{x}{y}=1\)
❏ \(x=y\)
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Re: If x^2=y^2, which of the following must be true?
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22 Jul 2025, 06:52
22 Jul 2025, 06:52
1
x^2 and y^2 are equal
option 1 |x| - |y| = 0 true cuz the mod strips off any -ve sign in them
option 2 x\y = 1 not necessarily true cuz x and y may have different signs
option 3 x = y not necessarily true cuz of the same reason given above
kudos is appreciated
option 1 |x| - |y| = 0 true cuz the mod strips off any -ve sign in them
option 2 x\y = 1 not necessarily true cuz x and y may have different signs
option 3 x = y not necessarily true cuz of the same reason given above
kudos is appreciated
Re: If x^2=y^2, which of the following must be true?
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23 Jul 2025, 04:00
23 Jul 2025, 04:00
Expert Reply
Given the equation $\(x^2=y^2\)$, let's analyze the options:
1. $\(|x|-|y|=0\)$
Since $\(x^2=y^2\)$, taking the square root of both sides gives $\(|x|=|y|\)$.
Thus, $\(|x|-|y|=0\)$ is true.
2. $\(\frac{x}{y}=1\)$
This implies $x=y$, but from $\(x^2=y^2\)$, either $\(x=y\)$ or $\(x=-y\)$.
So, this is not necessarily true.
3. $\(x=y\)$
Again, from $\(x^2=y^2\)$, you only know $\(x= \pm y\)$, so $\(x=y\)$ is not necessarily true.
Conclusion:
- The only must-be-true statement is $\(|x|-|y|=0\)$.
1. $\(|x|-|y|=0\)$
Since $\(x^2=y^2\)$, taking the square root of both sides gives $\(|x|=|y|\)$.
Thus, $\(|x|-|y|=0\)$ is true.
2. $\(\frac{x}{y}=1\)$
This implies $x=y$, but from $\(x^2=y^2\)$, either $\(x=y\)$ or $\(x=-y\)$.
So, this is not necessarily true.
3. $\(x=y\)$
Again, from $\(x^2=y^2\)$, you only know $\(x= \pm y\)$, so $\(x=y\)$ is not necessarily true.
Conclusion:
- The only must-be-true statement is $\(|x|-|y|=0\)$.
