Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 26 Aug 2016, 03:22

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Math question: Quite easy (maybe at least for you ;))

Author Message
TAGS:

Hide Tags

Intern
Joined: 06 Jan 2013
Posts: 8
Followers: 0

Kudos [?]: 1 [1] , given: 7

Math question: Quite easy (maybe at least for you ;)) [#permalink]

Show Tags

06 Jan 2013, 04:42
1
KUDOS
Hey Guys,

as I have found this forum today I would like to share my thoughts on the GMAT with you. I´ve began preparing for the test about a week ago and right now I´m still fighting easy problems.

I got a qestion that needs two equations two be created. I got the first equation, which is:

\sqrt{3-2x} = \sqrt{2x}+1

When I square both sides, I do get

3-2x = ?

My problem is that I don´t know any rule that leads to the correct term on the right side, which Is (as indicated in the explanations)

3-2x = 2x+2*\sqrt{2x}+1

Anyone any idea how this works?

Maybe some of you can help me with this.

Max
Current Student
Joined: 02 Jan 2013
Posts: 57
GMAT 1: 750 Q51 V40
GPA: 3.2
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 48 [0], given: 2

Re: Math question: Quite easy (maybe at least for you ;)) [#permalink]

Show Tags

06 Jan 2013, 06:02
Hi there, Try squaring the equation one more time:

$$\sqrt{3-2x} = \sqrt{2x} -1$$

Squaring both sides:
$$3-2x = 2x - 2.\sqrt{2x} +1$$
=> $$\sqrt{2x} =2x-1$$
Squaring both sides once again:

$$2x = 4 x^{2} -4x + 1$$
=> $$4 x^{2} -6x +1 = 0$$
=> $$x =\frac{3+- \sqrt{5}}{4}$$

Now for the tricky part. Since you squared a couple of times the original equation you certainly changed the nature of the equation (meaning, you may have inserted extra solutions that aren't in the original equation). So, you have to test your solutions in the original equation to see which ones still aply.

For the solution $$k = \frac{3- \sqrt{5}}{4}$$ you get that $$\sqrt{2k}-1$$is negative. Which is no good, since the left side of the original equation has to be always positive. The only solution that fits is

$$x = \frac{3+\sqrt{5}}{4}$$
Cheers!
BSchool Forum Moderator
Joined: 13 Dec 2012
Posts: 194
Followers: 7

Kudos [?]: 103 [0], given: 29

Re: Math question: Quite easy (maybe at least for you ;)) [#permalink]

Show Tags

06 Jan 2013, 06:11
maxkay47 wrote:
Hey Guys,

as I have found this forum today I would like to share my thoughts on the GMAT with you. I´ve began preparing for the test about a week ago and right now I´m still fighting easy problems.

I got a qestion that needs two equations two be created. I got the first equation, which is:

\sqrt{3-2x} = \sqrt{2x}+1

When I square both sides, I do get

3-2x = ?

My problem is that I don´t know any rule that leads to the correct term on the right side, which Is (as indicated in the explanations)

3-2x = 2x+2*\sqrt{2x}+1

Anyone any idea how this works?

Maybe some of you can help me with this.

Max

3 - 2x =( \sqrt{2x} + 1) * ( \sqrt{2x} + 1)

= 2x + \sqrt{2x} + \sqrt{2x} + 1

= 2x + 2 \sqrt{2x} + 1
_________________

Blog: The MBA Journey of an African Doctor

Blog updated: July 27, 2014

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6830
Location: Pune, India
Followers: 1923

Kudos [?]: 11936 [0], given: 221

Re: Math question: Quite easy (maybe at least for you ;)) [#permalink]

Show Tags

08 Jan 2013, 21:27
maxkay47 wrote:
Hey Guys,

as I have found this forum today I would like to share my thoughts on the GMAT with you. I´ve began preparing for the test about a week ago and right now I´m still fighting easy problems.

I got a qestion that needs two equations two be created. I got the first equation, which is:

\sqrt{3-2x} = \sqrt{2x}+1

When I square both sides, I do get

3-2x = ?

My problem is that I don´t know any rule that leads to the correct term on the right side, which Is (as indicated in the explanations)

3-2x = 2x+2*\sqrt{2x}+1

Anyone any idea how this works?

Maybe some of you can help me with this.

Max

How do you square a sum of two terms?

$$(a + b)^2 = a^2 + 2*a*b + b^2$$ Use this. If you don't know this, check out an algebra book first. This is a basic algebraic identity and you need to know this and similar identities for GMAT.

$$(\sqrt{2x}+1)^2 = (\sqrt{2x})^2+2*\sqrt{2x}*1+1^2$$
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Re: Math question: Quite easy (maybe at least for you ;))   [#permalink] 08 Jan 2013, 21:27
Similar topics Replies Last post
Similar
Topics:
Is there an easy way to solve this question? 0 30 Aug 2015, 12:50
2 Why You Should Do the Math on Data Sufficiency GMAT Questions 0 15 Apr 2015, 05:01
Need simple and easy maths tips 2 21 Mar 2013, 23:05
Kaplan GMAT Math Workbook: Too Easy? 3 02 Sep 2010, 17:50
Math Question 6 16 Feb 2009, 17:10
Display posts from previous: Sort by