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(11+1/11)^2(111/11)^2=?
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23 Jun 2017, 01:12
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\((11+\frac{1}{11})^2(11\frac{1}{11})^2=?\) A. 2 B. 3 C. 4 D. 5 E. 9
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Re: (11+1/11)^2(111/11)^2=?
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23 Jun 2017, 01:35
MathRevolution wrote: \((11+\frac{1}{11})^2(11\frac{1}{11})^2=?\) A. 2 B. 3 C. 4 D. 5 E. 9 Let \((11+\frac{1}{11}) = x\)
and \((11\frac{1}{11}) = y\)
\((11+\frac{1}{11})^2(11\frac{1}{11})^2 = x^2  y^2 = (x+y)(xy)\)
\((x+y)(xy) = (11+\frac{1}{11} + 11\frac{1}{11})(11+\frac{1}{11}  (11\frac{1}{11}))\)
\((11+11) (11  11+\frac{1}{11}+\frac{1}{11}) = (22) (\frac{1+1}{11})\)
\((22)(\frac{2}{11})\) \(= 2*2 = 4\) . Answer (C)...



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(11+1/11)^2(111/11)^2=?
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23 Jun 2017, 02:02
\(a^2b^2=(a+b)(ab)\) \(a=11+\frac{1}{11}\) \(b=11\frac{1}{11}\) Solving , \(22\frac{2}{11}\) 4
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Re: (11+1/11)^2(111/11)^2=?
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23 Jun 2017, 02:24
We need to find out the value of the expression \((11+\frac{1}{11})^2(11\frac{1}{11})^2\) Let 11 = a, \(\frac{1}{11}\) = b So the expression becomes \((a+b)^2  (ab)^2\) = \(a^2 + 2ab + b^2  (a^2  2ab + b^2)\) =4ab Since \((a+b)^2 = a^2 + 2ab + b^2 and (ab)^2 = a^2  2ab + b^2\) Substituting the values of a and b, we get the value of expression to be 4(Option C)
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Re: (11+1/11)^2(111/11)^2=?
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23 Jun 2017, 08:36
MathRevolution wrote: \((11+\frac{1}{11})^2(11\frac{1}{11})^2=?\) A. 2 B. 3 C. 4 D. 5 E. 9 \((11+\frac{1}{11})^2\) = \(11^2 + 1/11^2 + 2*11*\frac{1}{11}\) = \(121 + \frac{1}{121} + 2\) = \(123 + \frac{1}{121}\) \((11\frac{1}{11})^2\) = \(11^2 + 1/11^2  2*11*\frac{1}{11}\) = \(121 + \frac{1}{121}  2\) = \(119 + \frac{1}{121}\) So, \((11+\frac{1}{11})^2(11\frac{1}{11})^2=?\) = \(123 + 1/121\)  \(119 + 1/121\) = \(123  119 + \frac{1}{121}  \frac{1}{121}\) = \(4\) Hence, answer will be (C)
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Re: (11+1/11)^2(111/11)^2=?
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23 Jun 2017, 11:08
(11+1/11)^2(111/11)^2 is in the form of a^2  b^2 = (a+b)(ab), =(11+1/11+111/11)(11+1/1111+1/11), =(22)(2/11), =4 Ans = C



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Re: (11+1/11)^2(111/11)^2=?
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23 Jun 2017, 11:29
\((11+\frac{1}{11})^2(11\frac{1}{11})^2=?\) Simplifying in the form of (a+b)^2  (ab)^2 After substituting the values we get: 11^2 + 2 + (1/11)^2  11^2 + 2  (1/11)^2 Cancelling the terms we are left with 2+2 = 4 Hence, the answer is C = 4
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Re: (11+1/11)^2(111/11)^2=?
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23 Jun 2017, 11:52
This can be written as = \((a + b)^{2}\)  \(( a  b)^{2}\) = \(a^{2}\) + \(b^{2}\) + 2ab  \(a^{2}\) \(b^{2}\) + 2ab = 4ab where a = 11 & b = \(\frac{1}{11}\) = 4 * 11 * \(\frac{1}{11}\) = 4 = C
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Re: (11+1/11)^2(111/11)^2=?
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25 Jun 2017, 18:17
==> You get \((11+\frac{1}{11})^2(11\frac{1}{11})^2=[(11+\frac{1}{11})(11\frac{1}{11})][(11+\frac{1}{11})+(11\frac{1}{11})]= \frac{2}{11}(22)=4.\) The answer is C. Answer: C
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Re: (11+1/11)^2(111/11)^2=?
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25 Jun 2017, 23:41
imo C We can solve this problem by using identity (a+b)^2=a^2+b^2+2ab (ab)^2=a^2+b^22ab
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Re: (11+1/11)^2(111/11)^2=?
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26 Jun 2017, 17:56
MathRevolution wrote: \((11+\frac{1}{11})^2(11\frac{1}{11})^2=?\) A. 2 B. 3 C. 4 D. 5 E. 9 We can use the difference of squares concept, for which we let x = 11 + 1/11 and y =11  1/11, so we have: x^2  y^2 (x  y)(x + y) [(11 + 1/11)  (11  1/11)][(11 + 1/11) + (11  1/11)] (2/11)(22) = 4 Answer: C
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Re: (11+1/11)^2(111/11)^2=?
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27 Jun 2018, 07:46
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