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# If (x^2 + 4)^(1/2) = x + h, what is the value of x?

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Joined: 02 Sep 2009
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If (x^2 + 4)^(1/2) = x + h, what is the value of x? [#permalink]

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03 Apr 2018, 21:39
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If $$\sqrt{x^2 + 4} = x + h$$, what is the value of x?

(1) h = 2
(2) h^2 = 4
[Reveal] Spoiler: OA

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Joined: 05 Feb 2016
Posts: 107
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: If (x^2 + 4)^(1/2) = x + h, what is the value of x? [#permalink]

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03 Apr 2018, 23:51
Bunuel wrote:
If $$\sqrt{x^2 + 4} = x + h$$, what is the value of x?

(1) h = 2
(2) h^2 = 4

From1:
h=2
$$\sqrt{x^2 + 4} = x + 2$$
squaring both sides:$$x^2 + 4= (x + 2)^2$$
solving this we get x=0

sufficient.

From2:
h=2,-2
$$\sqrt{x^2 + 4} = x + 2$$ & $$\sqrt{x^2 + 4} = x - 2$$

solving both we will get x=0

so sufficient

hence D
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Re: If (x^2 + 4)^(1/2) = x + h, what is the value of x? [#permalink]

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Updated on: 04 Apr 2018, 02:00
Bunuel wrote:
If $$\sqrt{x^2 + 4} = x + h$$, what is the value of x?

(1) h = 2
(2) h^2 = 4

x+2=x+h

h=2 and x =0

Stmnt 1:

x+2 = x+2

True

Stmnt 2:

h^2 = 4
h = + or - 2

False

Ans : A

Sent from my SM-G925I using GMAT Club Forum mobile app

Originally posted by nishore1 on 04 Apr 2018, 00:21.
Last edited by nishore1 on 04 Apr 2018, 02:00, edited 2 times in total.
BSchool Forum Moderator
Joined: 07 Jan 2016
Posts: 717
Location: India
GMAT 1: 710 Q49 V36
Re: If (x^2 + 4)^(1/2) = x + h, what is the value of x? [#permalink]

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04 Apr 2018, 00:22
Bunuel wrote:
If $$\sqrt{x^2 + 4} = x + h$$, what is the value of x?

(1) h = 2
(2) h^2 = 4

1) h=2

we can find a unique value
sufficient

2) h^2 = 4

h= 2 or -2

2 values of x

insufficient

(A)imo
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Joined: 15 Oct 2017
Posts: 124
Re: If (x^2 + 4)^(1/2) = x + h, what is the value of x? [#permalink]

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05 Apr 2018, 09:06
IMO D

The equation on simplifying becomes- h(2x+h) = 4.

1) h=2, substituting in our simplified equation we get x=0. Therefore, sufficient.

2) h=+/-2, substituting both values of h in our simplified equation we get x=0. Therefore sufficient.

Hence, D.
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Re: If (x^2 + 4)^(1/2) = x + h, what is the value of x? [#permalink]

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05 Apr 2018, 23:58
Bunuel wrote:
If $$\sqrt{x^2 + 4} = x + h$$, what is the value of x?

(1) h = 2
(2) h^2 = 4

A quick look at both statements tells us that we will have to deal with h=2 and h=-2. so we should input both these values in the question stem and check whether it satisfies or not. If we square both sides in question stem, we get: (x^2 + 4) = (x^2 + h^2 + 2xh). Or 4 = h^2 + 2xh

Lets put h=2, we get: 4 = 4 + 4x or 4x = 0 or x=0

Lets put h=-2, we get: 4 = 4 - 4x or -4x=0 or x=0.

In any case, it gives us the same value of x, which is 0. So either statement alone is sufficient. hence D answer
Re: If (x^2 + 4)^(1/2) = x + h, what is the value of x?   [#permalink] 05 Apr 2018, 23:58
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