If x > 0, What is the least possible value of -2âˆš(5x) +

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Mon May 20, 2019 4:33 am

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If x > 0, What is the least possible value of -2âˆš(5x) + x + 9 ?

A. 0
B. 1
C. âˆš5
D. 4
E. 9

OA D

Source: e-GMAT

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Source: Beat The GMAT — Problem Solving | Mon May 20, 2019 4:33 am

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by Scott@TargetTestPrep » Tue May 21, 2019 6:26 pm

BTGmoderatorDC wrote:If x > 0, What is the least possible value of -2âˆš(5x) + x + 9 ?

A. 0
B. 1
C. âˆš5
D. 4
E. 9

OA D

Source: e-GMAT

Notice that (âˆšx - âˆš5)^2 = (âˆšx)^2 + (âˆš5)^2 - 2(âˆšx)(âˆš5) = x + 5 - 2âˆš(5x). Therefore,

-2âˆš(5x) + x + 9 = (âˆšx - âˆš5)^2 + 4

Since the minimum value of (âˆšx - âˆš5)^2 is 0, then the minimum value of -2âˆš(5x) + x + 9 is:

(âˆšx - âˆš5)^2 + 4 = 0 + 4 = 4

Answer: D

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