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√r + 2/√r = 4. What is the value of r + 4/r?

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Math Revolution GMAT Instructor
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√r + 2/√r = 4. What is the value of r + 4/r?  [#permalink]

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New post 26 Mar 2019, 02:09
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

63% (01:09) correct 37% (01:26) wrong based on 27 sessions

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[GMAT math practice question]

\(√r + \frac{2}{√r} = 4\). What is the value of \(r + \frac{4}{r}\)?

\(A. 12\)
\(B. 14\)
\(C. 16\)
\(D. 32\)
\(E. 64\)

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Re: √r + 2/√r = 4. What is the value of r + 4/r?  [#permalink]

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New post 26 Mar 2019, 03:31
MathRevolution wrote:
[GMAT math practice question]

\(√r + \frac{2}{√r} = 4\). What is the value of \(r + \frac{4}{r}\)?

\(A. 12\)
\(B. 14\)
\(C. 16\)
\(D. 32\)
\(E. 64\)


Apply the following identity:
\((a+b)² = a² + b² + 2ab\)

\(√r + \frac{2}{√r} = 4\)
\((√r + \frac{2}{√r})² = 4²\)
\((√r)² + (\frac{2}{√r})² + 2(√r)(\frac{2}{√r}) = 16\)
\(r + \frac{4}{r} + 4 = 16\)
\(r + \frac{4}{r} = 12\)

.
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√r + 2/√r = 4. What is the value of r + 4/r?  [#permalink]

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New post 28 Mar 2019, 01:41
=>

\((√r + \frac{2}{√r})^2 = r + 2(√r)(\frac{2}{√r}) + \frac{4}{r} = r + \frac{4}{r} + 4 = 4^2 = 16\)
So, \(r + \frac{4}{r} = 16 -4 = 12.\)

Therefore, A is the answer.
Answer: A
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√r + 2/√r = 4. What is the value of r + 4/r?   [#permalink] 28 Mar 2019, 01:41
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