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If √x = x, then which of the following must be true?

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If √x = x, then which of the following must be true?  [#permalink]

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New post Updated on: 22 Mar 2013, 02:54
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A
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D
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If \(\sqrt{x}\) = x, then which of the following must be true?

A. x is positive
B. x=1
C. x^2>x
D. x is non-negative
E. None of the above

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Originally posted by emmak on 22 Mar 2013, 00:56.
Last edited by Bunuel on 22 Mar 2013, 02:54, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If √x=x , then which of the following must be true? x is  [#permalink]

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New post 22 Mar 2013, 01:34
emmak wrote:
If \(\sqrt{x}\)=x , then which of the following must be true?
a) x is positive
b) x=1
c) \(x^2\)>x
d) x is non-negative
e) none of the above


Square both the sides we get
x = x^2
x^2 - x= 0
x(x-1)=0
either x=0 or x=1
So, asnwer will be D

hope it helps!
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Re: If √x = x, then which of the following must be true?  [#permalink]

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New post 22 Mar 2013, 03:03
If \(\sqrt{x}= x\) , then which of the following must be true?

A. x is positive
B. x=1
C. x^2>x
D. x is non-negative
E. None of the above

We have that x is equal to the square root of some number (\(\sqrt{x}\)). Now, we know that the square root function cannot give negative result (\(\sqrt{{some \ expression}}\geq{0}\)), thus LHS (\(\sqrt{x}\)) is more than or equal to zero, which implies tha RHS (x) is also more than or equal to zero. Hence we have that \(x\geq{0}\).

Answer: D.

Or simply be solving: \(\sqrt{x}= x\) --> \(x=x^2\) --> \(x(x-1)=0\) --> \(x=0\) or \(x=1\).

Answer: D.
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Re: If √x = x, then which of the following must be true?  [#permalink]

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New post 17 Feb 2018, 03:39
Square it on both sides
x^2=x
x^2-x=0
x(x-1)=0
x=0,1
So D should be the answer because this is a "must be true" question
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Re: If √x = x, then which of the following must be true?  [#permalink]

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New post 19 Feb 2019, 16:27
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Re: If √x = x, then which of the following must be true?   [#permalink] 19 Feb 2019, 16:27
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