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16 Sep 2014, 00:18
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A
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Difficulty:
25%
(medium)
Question Stats:
67% (01:00) correct
33%
(01:03)
wrong
based on 882
sessions
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Date
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What is the value of \(x^2\)?
(1) \(x = \sqrt{2x - 1}\)
(2) \(x^2 = x^3\)
(1) \(x = \sqrt{2x - 1}\)
(2) \(x^2 = x^3\)
16 Sep 2014, 00:18
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Official Solution:
What is the value of \(x^2\)?
(1) \(x = \sqrt{2x - 1}\)
Square:
\(x^2 = 2x - 1\)
\(x^2 - 2x + 1 = 0\)
\((x-1)^2 = 0\)
\(x -1 = 0\)
\(x = 1\)
Thus, \(x^2 = 1\). Sufficient/
(2) \(x^2 = x^3\):
\(x^2 - x^3 = 0\)
\(x^2 (1 - x) = 0\)
\(x = 0\) or \(x =1\).
Therefore, \(x^2 = 0\) or \(x^2 = 1\). Not sufficient.
Answer: A
What is the value of \(x^2\)?
(1) \(x = \sqrt{2x - 1}\)
Square:
\(x^2 = 2x - 1\)
\(x^2 - 2x + 1 = 0\)
\((x-1)^2 = 0\)
\(x -1 = 0\)
\(x = 1\)
Thus, \(x^2 = 1\). Sufficient/
(2) \(x^2 = x^3\):
\(x^2 - x^3 = 0\)
\(x^2 (1 - x) = 0\)
\(x = 0\) or \(x =1\).
Therefore, \(x^2 = 0\) or \(x^2 = 1\). Not sufficient.
Answer: A
General Discussion
03 Mar 2023, 10:58
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
