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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
57% (00:53) correct
43%
(00:51)
wrong
based on 831
sessions
History
Date
Time
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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
A. x is positive
B. x=1
C. x^2>x
D. x is non-negative
E. None of the above
Updated on: 14 May 2023, 02:34
Originally posted by BrushMyQuant on 22 Mar 2013, 01:34.
Last edited by BrushMyQuant on 14 May 2023, 02:34, edited 1 time in total.
Last edited by BrushMyQuant on 14 May 2023, 02:34, edited 1 time in total.
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Given that \(\sqrt{x}\)=x and we need to find which of the following must be true?
\(\sqrt{x}\)=x
Squaring both the sides we get:
x = \(x^2\)
\(x^2\) - x= 0
x(x-1)=0
=> x=0 or x=1
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Roots
\(\sqrt{x}\)=x
Squaring both the sides we get:
x = \(x^2\)
\(x^2\) - x= 0
x(x-1)=0
=> x=0 or x=1
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Roots
General Discussion
22 Mar 2013, 03:03
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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
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.
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.
