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31 Mar 2021, 02:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
80% (01:24) correct
20%
(02:05)
wrong
based on 351
sessions
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Date
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Not Attempted Yet
\((11+\frac{1}{11})^2-(11-\frac{1}{11})^2=?\)
A. 2
B. 3
C. 4
D. 5
E. 9
A. 2
B. 3
C. 4
D. 5
E. 9
31 Mar 2021, 02:08
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Bunuel
CONCEPT:
\((a+b)^2 - (a-b)^2 = a^2+b^2 + 2ab - a^2 -b^2 +2ab = 4ab\)
i.e. \((11+\frac{1}{11})^2-(11-\frac{1}{11})^2=4*11*(\frac{1}{11}) = 4\)
Answer: Option C
General Discussion
Bunuel
We know that, \((a+b) * (a-b)\) = \(a^2 - b^2\)
which also means that \(a^2 - b^2\) = \((a+b) * (a-b)\)
Consider \((11 + \frac{1}{11})^2\) as a and \((11-\frac{1}{11})^2\) as b.
So, \(a^2 - b^2\) = \((a + b)(a-b)\)
\((11+\frac{1}{11})^2 - (11-\frac{1}{11})^2\) = \((11 + \frac{1}{11} + 11 - \frac{1}{11}) (11 + \frac{1}{11} - 11 + \frac{1}{11})\)
=\(22 * \frac{2}{11}\)
=\(4\)
