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If (2 - sqrt(5))x = -1, then x =

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If (2 - sqrt(5))x = -1, then x = [#permalink] New post 25 Nov 2010, 15:17
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Question Stats:

74% (01:53) correct 26% (01:16) wrong based on 77 sessions
If (2-\sqrt{5})x = -1, then x=

A. 2 + sqrt(5)
B. 1 + (sqrt(5)/2
C. 1 - (sqrt(5)/2
D. 2 - sqrt(5)
E. -2 - sqrt(5)
[Reveal] Spoiler: OA

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Last edited by Bunuel on 02 Jul 2013, 23:43, edited 1 time in total.
Renamed the topic and edited the question.
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Re: PS: if ( 2 - sqrt(5))x = -1, then x = [#permalink] New post 25 Nov 2010, 15:28
Expert's post
vrajesh wrote:
if ( 2 - sqrt(5))x = -1, then x =

A. 2 + sqrt(5)
B. 1 + (sqrt(5)/2
C 1 - (sqrt(5)/2
D. 2 - sqrt(5)
E. -2 - sqrt(5)


Please explain. I can't seem to figure it out


Please read and follow:
writing-mathematical-symbols-in-posts-72468.html
how-to-improve-the-forum-search-function-for-others-99451.html

Question should be: If (2-\sqrt{5})x = -1, then x=

(2-\sqrt{5})x = -1 --> x=-\frac{1}{2-\sqrt{5}}=\frac{1}{\sqrt{5}-2}. Multiply both denominator and nominator by \sqrt{5}+2:

x=\frac{\sqrt{5}+2}{(\sqrt{5}-2)(\sqrt{5}+2)}=\frac{\sqrt{5}+2}{\sqrt{5}^2-2^2}=\frac{\sqrt{5}+2}{5-4}=\sqrt{5}+2.

Answer: A.
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Re: PS: if ( 2 - sqrt(5))x = -1, then x = [#permalink] New post 27 Nov 2010, 12:16
Geez, i feel stupid.... explain me plz the following stages:
1. x=-\frac{1}{2-\sqrt{5}}=\frac{1}{\sqrt{5}-2}
2. the last stage.

Thanks for ur time.
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Re: If (2 - sqrt(5))x = -1, then x = [#permalink] New post 17 Jul 2014, 02:02
(2 - \sqrt{5}) x = -1

x = \frac{1}{\sqrt{5} - 2}

Multiple RHS numerator & denominator by \sqrt{5} + 2

x = \frac{\sqrt{5} + 2}{(\sqrt{5} + 2) (\sqrt{5} - 2)}

x = \frac{\sqrt{5} + 2}{5-4}

x = \sqrt{5} + 2

Answer = A
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Re: If (2 - sqrt(5))x = -1, then x =   [#permalink] 17 Jul 2014, 02:02
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