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# The value of (1/x)-(4/√x)+4 is least when x =

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Senior Manager
Joined: 25 Dec 2018
Posts: 455
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
The value of (1/x)-(4/√x)+4 is least when x =  [#permalink]

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19 Apr 2019, 08:54
2
00:00

Difficulty:

55% (hard)

Question Stats:

50% (01:57) correct 50% (02:14) wrong based on 30 sessions

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The value of (1/x)-(4/√x)+4 is least when x =

A. 1/√6
B. 1/4
C. 1/√2
D. 1/2
E. 1
Math Expert
Joined: 02 Aug 2009
Posts: 7756
Re: The value of (1/x)-(4/√x)+4 is least when x =  [#permalink]

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19 Apr 2019, 23:55
1
mangamma wrote:
The value of (1/x)-(4/√x)+4 is least when x =

A. 1/√6
B. 1/4
C. 1/√2
D. 1/2
E. 1

Since we have √x, X has to be positive, so let x=y^2..
So (1/x)-(4/√x)+4=(1/y^2)-(4/y)+4=$$\frac{4y^2-4y+1}{y^2}=\frac{(2y-1)^2}{y^2}$$..
Least value here will be 0 when numerator is 0. (2y-1)^2 will be 0 at y=1/2..
Thus x=y^2=(1/2)^2=1/4..

B

If you are clueless, just see here X is, it is in the denominator...
To make the term lowest, we have to maximize the - term, that is -(4/√x).
And X is the denominator, so we have to make the denominator the least.
In choices 1/4 is the least.
Need not be true always, but will increase the probability of answering correctly if you have nowhere to go.
_________________
Re: The value of (1/x)-(4/√x)+4 is least when x =   [#permalink] 19 Apr 2019, 23:55
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