Last visit was: 20 Jul 2024, 09:46 It is currently 20 Jul 2024, 09:46
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
avatar
Intern
Intern
Joined: 25 Jul 2009
Posts: 5
Own Kudos [?]: 50 [19]
Given Kudos: 2
Send PM
Math Expert
Joined: 02 Sep 2009
Posts: 94430
Own Kudos [?]: 642521 [2]
Given Kudos: 86708
Send PM
User avatar
Manager
Manager
Joined: 08 Nov 2010
Posts: 202
Own Kudos [?]: 502 [0]
Given Kudos: 161
 Q50  V41
GPA: 3.9
WE 1: Business Development
Send PM
avatar
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1558
Own Kudos [?]: 7299 [0]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
Re: If (2 - sqrt(5))x = -1, then x = [#permalink]
\((2 - \sqrt{5}) x = -1\)

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

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
Intern
Intern
Joined: 31 Jan 2021
Posts: 45
Own Kudos [?]: 34 [1]
Given Kudos: 99
Location: Bangladesh
GMAT 1: 760 Q50 V44
Send PM
Re: If (2 - sqrt(5))x = -1, then x = [#permalink]
1
Kudos
(2 - sqrt(5))x = -1

Let's multiply both sides by (2 + sqrt(5)):

(2 - sqrt(5)) (2 + sqrt(5))x = -1(2 + sqrt(5))

(4-5)x = -1(2 + sqrt(5))

x = (2 + sqrt(5))
Senior Manager
Senior Manager
Joined: 22 Aug 2020
Posts: 472
Own Kudos [?]: 355 [0]
Given Kudos: 30
Location: India
Concentration: International Business, Finance
GPA: 4
WE:Project Management (Energy and Utilities)
Send PM
Re: If (2 - sqrt(5))x = -1, then x = [#permalink]
vrajesh wrote:
If \((2-\sqrt{5})x = -1\), then \(x=\)

A. \(2 + \sqrt{5}\)
B. \(\frac{1 + \sqrt{5}}{2}\)
C. \(\frac{1 - \sqrt{5}}{2}\)
D. \(2 - \sqrt{5}\)
E. \(-2 - \sqrt{5}\)


\((2-\sqrt{5})x = -1\)

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

\(x = \frac{-1}{(2-\sqrt{5})} * \frac{(2+\sqrt{5})}{(2+\sqrt{5})}\)

\(x = \frac{-1 (2+\sqrt{5})}{(4-5)}\)

\(x = \frac{-1 (2+\sqrt{5})}{(-1)}\)

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

Ans A
Senior Manager
Senior Manager
Joined: 01 Mar 2015
Posts: 410
Own Kudos [?]: 937 [0]
Given Kudos: 42
Location: India
Send PM
Re: If (2 - sqrt(5))x = -1, then x = [#permalink]
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)


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

Rationalizing the denominator, we get
\(x =\frac{ -1(2+\sqrt{5})}{(4-5)}\) \(= 2+\sqrt{5}\)

Hence, OA is (A).
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1803
Own Kudos [?]: 2145 [0]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Send PM
If (2 - sqrt(5))x = -1, then x = [#permalink]
Expert Reply
Top Contributor
↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




Given that \((2-\sqrt{5})x\) = -1 and we need to find the value of x

\((2-\sqrt{5})x\) = -1
=> x = \(\frac{-1}{2-\sqrt{5} }\) = \(\frac{1 }{ \sqrt{5} - 2}\)

Multiplying numerator and denominator with \(\sqrt{5} + 2\) we get

x = \(\frac{1 * \sqrt{5} + 2}{ (\sqrt{5} - 2)*(\sqrt{5} + 2)}\)
= \(\frac{\sqrt{5} + 2}{(\sqrt{5})^2 - 2^2}\) = \(\frac{\sqrt{5} + 2}{5 - 4}\) = \(\sqrt{5} + 2\)

So, Answer will be A
Hope it helps!

Watch the following video to learn How to Rationalize Roots

GMAT Club Bot
If (2 - sqrt(5))x = -1, then x = [#permalink]
Moderator:
Math Expert
94430 posts