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

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

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New post 06 Feb 2019, 01:41
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

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

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

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New post 06 Feb 2019, 01:44
1
Just substitute the values in the options given
B is the right answer
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If (x+ 3)^(1/2) = x^(1/2) + 3^(1/2), then x is  [#permalink]

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New post 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.

B is the correct answer.

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.
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Re: If (x+ 3)^(1/2) = x^(1/2) + 3^(1/2), then x is  [#permalink]

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New post 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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