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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]  21 Mar 2013, 23:56
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Question Stats:

60% (01:38) correct 40% (00:35) wrong based on 40 sessions
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
[Reveal] Spoiler: OA

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Last edited by Bunuel on 22 Mar 2013, 01:54, edited 1 time in total.
Renamed the topic and edited the question.
Status: If you think you can, then eventually you WILL!
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Kudos [?]: 192 [0], given: 39

Re: If √x=x , then which of the following must be true? x is [#permalink]  22 Mar 2013, 00:34
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]  22 Mar 2013, 02:03
Expert's post
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}.

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

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Re: If √x = x, then which of the following must be true?   [#permalink] 22 Mar 2013, 02:03
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