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

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by Max@Math Revolution » Tue Mar 26, 2019 12:52 am

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[GMAT math practice question]

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

A. 12
B. 14
C. 16
D. 32
E. 64
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by GMATGuruNY » Tue Mar 26, 2019 2:13 am
Max@Math Revolution wrote:[GMAT math practice question]

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

A. 12
B. 14
C. 16
D. 32
E. 64
(a+b)² = a² + b² + 2ab

√r + 2/√r = 4
(√r + 2/√r)² = 4²
(√r)² + (2/√r)² + 2(√r)(2/√r) = 16
r + 4/r + 4 = 16
r + 4/r = 12

The correct answer is A.
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by Max@Math Revolution » Thu Mar 28, 2019 12:35 am
=>

(√r + 2/√r)^2 = r + 2(√r)(2/√r) + 4/r = r + 4/r + 4 = 4^2 = 16
So, r + 4/r = 16 -4 = 12.

Therefore, A is the answer.
Answer: A
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