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12 Oct 2018, 08:38
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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:
25%
(medium)
Question Stats:
88% (00:35) correct
12%
(01:20)
wrong
based on 25
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[Math Revolution GMAT math practice question]
If \(x+(\frac{1}{x})=4\), what is the value of \(x^2+(\frac{1}{x^2})\)?
\(A. 4\)
\(B. 10\)
\(C. 12\)
\(D. 14\)
\(E. 16\)
If \(x+(\frac{1}{x})=4\), what is the value of \(x^2+(\frac{1}{x^2})\)?
\(A. 4\)
\(B. 10\)
\(C. 12\)
\(D. 14\)
\(E. 16\)
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Chethan92
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12 Oct 2018, 08:52
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\((a+b)^2\) = \(a^2\) + \(b^2\) +2ab.
Here a = x and b = \(\frac{1}{x}\).
Substituting this, we get.
\((x+\frac{1}{x})^2\) = \(x^2\) + \(\frac{1}{x}^2\) +2x\(\frac{1}{x}\).
16-2 = \(x^2\) + \(\frac{1}{x}^2\)
D is the answer.
Here a = x and b = \(\frac{1}{x}\).
Substituting this, we get.
\((x+\frac{1}{x})^2\) = \(x^2\) + \(\frac{1}{x}^2\) +2x\(\frac{1}{x}\).
16-2 = \(x^2\) + \(\frac{1}{x}^2\)
D is the answer.
12 Oct 2018, 12:43
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MathRevolution
FOCUS:
\(? = {x^2} + {1 \over {{x^2}}}\)
DATA:
\(x + {1 \over x} = 4\,\,\,\,\left( * \right)\)
FOCUS-DATA CONNECTION:
\(?\,\, = \,\,{x^2} + \underline 2 + {1 \over {{x^2}}} - \underline 2 \,\, = \,\,{\left( {x + {1 \over x}} \right)^2} - 2\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,\,{4^2} - 2 = 14\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
