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

Question

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

A. 0
B. 1
C. √5
D. 4
E. 9

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dhart · Answer

Either -2root5x + x + 9 decrase when -2root5x value is high
 to achieve 0,1 or postive root 5 is difficult
for e.g x=5 -2 root(5*5) +5+9= -10+14= 4

for x = 20 -2root (5*20)+20+9 = 9

least value 4 D

odionam · Answer

-2√(5x) + x + 9
can be written as X-2√(5x)+9 this can further square of square root of x - 2* 5 *x + sq of sqrt 5 + sq of sqrt 4 : 
(√x)^2 - 2*√x*√5 + (√5)^2 + √(4)^2
this became (√x-√5)^2 +4 1st part at minimum zero can't -ve so 4 is the answer.

tcocarogallart · Answer

Hi,  Bunuel !
Would you be so kind to throw some light into this, please

Bunuel · Answer

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

A. 0
B. 1
C. √5
D. 4
E. 9

We complete the square in terms of   \sqrt{x}  :

-2\sqrt{5x}+x+9=x-2\sqrt5\sqrt x+9  .

Now,

(\sqrt x-\sqrt5)^2=x-2\sqrt5\sqrt x+5  .

Therefore, rewrite 9 as 5 + 4 so that the first three terms form this square:

x-2\sqrt5\sqrt x+5+4=(\sqrt x-\sqrt5)^2+4  .

The square term ( (\sqrt x-\sqrt5)^2 ) is smallest when it equals 0, so the least possible value is 4.

Answer: D.

sagarrathee77 · Answer

My 1st Answer on this community.

my approach => Differentiate the equation, you will get the local minima point when slope ( which is the result of differentiation of the equation) = 0
thus d(9+x-2sqrt(5x))/dx = 1-sqrt(5)/sqrt(x)

putting this equal to 0, gives us x=5,

PUtting x=5 in the above equation, gives us the answer 4

tcocarogallart · Answer

That's exactly what I did too! But I don't think we are meant to work with those tools on the GMAT, are we? So I thought there would be a simpler/faster way

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

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