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10 Nov 2023, 04:48
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
60% (02:21) correct
41%
(02:43)
wrong
based on 200
sessions
History
Date
Time
Result
Not Attempted Yet
If \(\sqrt{x^2+9}+\sqrt{x^2-3}=6\), what is the value of \(\sqrt{x^2+9}-\sqrt{x^2-3}\)?
A. \(1\)
B. \(2\)
C. \(3\)
D. \(4\)
E. \(5\)
A. \(1\)
B. \(2\)
C. \(3\)
D. \(4\)
E. \(5\)
12 Nov 2023, 09:37
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Bunuel
OA is B
Posted from my mobile device
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General Discussion
08 Mar 2024, 23:51
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The point is that you have to recognise \(\sqrt{x^2 + 9} + \sqrt{x^2 - 3}\) and \(\sqrt{x^2 + 9} - \sqrt{x^2 - 3}\) are a lot like the property \((a)^2 - (b)^2 = (a+b)(a-b)\)
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So, \((\sqrt{x^2 + 9} + \sqrt{x^2 - 3})(\sqrt{x^2 + 9} - \sqrt{x^2 - 3})\) = \((\sqrt{x^2 + 9})^2\) - \((\sqrt{x^2 - 3})^2\). Solve and you will get your answer as:
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\((6)(\sqrt{x^2 + 9} - \sqrt{x^2 - 3}) = 12\)
Therefore, the answer = 2
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So, \((\sqrt{x^2 + 9} + \sqrt{x^2 - 3})(\sqrt{x^2 + 9} - \sqrt{x^2 - 3})\) = \((\sqrt{x^2 + 9})^2\) - \((\sqrt{x^2 - 3})^2\). Solve and you will get your answer as:
.
.
.
\((6)(\sqrt{x^2 + 9} - \sqrt{x^2 - 3}) = 12\)
Therefore, the answer = 2
