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# If (x+ 3)^(1/2) = x^(1/2) + 3^(1/2), then x is

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
If (x+ 3)^(1/2) = x^(1/2) + 3^(1/2), then x is  [#permalink]

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06 Feb 2019, 01:41
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:17) correct 25% (00:53) wrong based on 15 sessions

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If $$\sqrt{x+ 3} = \sqrt{x} + \sqrt{3}$$, then x is

A. −3
B. 0
C. $$\sqrt{3}$$
D. 3
E. 9

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Manager
Joined: 11 Dec 2013
Posts: 121
Location: India
GMAT Date: 03-15-2015
WE: Education (Education)
Re: If (x+ 3)^(1/2) = x^(1/2) + 3^(1/2), then x is  [#permalink]

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06 Feb 2019, 01:44
1
Just substitute the values in the options given
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Joined: 31 Oct 2013
Posts: 1475
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If (x+ 3)^(1/2) = x^(1/2) + 3^(1/2), then x is  [#permalink]

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Updated on: 06 Feb 2019, 02:31
Bunuel wrote:
If $$\sqrt{x+ 3} = \sqrt{x} + \sqrt{3}$$, then x is

A. −3
B. 0
C. $$\sqrt{3}$$
D. 3
E. 9

Given,

$$\sqrt{x+ 3} = \sqrt{x} + \sqrt{3}$$

($$\sqrt{x+ 3})^2 = (\sqrt{x} + \sqrt{3}$$)^2

$$x + 3 = (\sqrt{x})^2 + 2\sqrt{x}\sqrt{3} + (\sqrt{3})^2$$

x + 3 - x - 3 = 2$$\sqrt{3x}$$

$$0 = 2\sqrt{3x}$$

$$0 = \sqrt{3x}$$

$$( 0)^2 = (\sqrt{3x})^2$$

0 = 3x

x = 0.

Originally posted by KSBGC on 06 Feb 2019, 01:52.
Last edited by KSBGC on 06 Feb 2019, 02:31, edited 1 time in total.
Manager
Joined: 11 Dec 2013
Posts: 121
Location: India
GMAT Date: 03-15-2015
WE: Education (Education)
Re: If (x+ 3)^(1/2) = x^(1/2) + 3^(1/2), then x is  [#permalink]

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06 Feb 2019, 02:24
selim
You made a mistake in the third step -- Its not (x-3)

You can substitute x=3 and see , the equation fails
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Re: If (x+ 3)^(1/2) = x^(1/2) + 3^(1/2), then x is   [#permalink] 06 Feb 2019, 02:24
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