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

 It is currently 05 Feb 2016, 19:52

### 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

# How many solutions does equation (x^2-25)^2=x^2-10x+25 have

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Director
Joined: 17 Oct 2005
Posts: 932
Followers: 1

Kudos [?]: 115 [0], given: 0

How many solutions does equation (x^2-25)^2=x^2-10x+25 have [#permalink]  22 Apr 2006, 17:07
How many solutions does equation (x^2-25)^2=x^2-10x+25 have?
Manager
Joined: 20 Mar 2005
Posts: 201
Location: Colombia, South America
Followers: 1

Kudos [?]: 9 [0], given: 0

Re: squared equations [#permalink]  22 Apr 2006, 17:29
joemama142000 wrote:
How many solutions does equation (x^2-25)^2=x^2-10x+25 have?

Using the fundamental theorem of algebra I would say 4, but not all of them necesarily real or different.
Manager
Joined: 20 Nov 2004
Posts: 108
Followers: 0

Kudos [?]: 3 [0], given: 0

Re: squared equations [#permalink]  23 Apr 2006, 00:31
conocieur wrote:
Using the fundamental theorem of algebra I would say 4, but not all of them necesarily real or different.

That's correct. In this case, all are real, but we have twice +5.
(x^2 - 25)^2 = x^2 - 10x + 25
x^4 - 51x^2 - 10x + 600 = 0
(x+5)(x+5)(x-4)(x-6) = 0

x = - 5 OR x = +4 OR x = +6
Senior Manager
Joined: 09 Mar 2006
Posts: 445
Followers: 1

Kudos [?]: 8 [0], given: 0

[#permalink]  23 Apr 2006, 07:19
the answer is right , but the solution is wrong
try to substitute your answers into the actual equation...

my solution is:
(x - 5 ) ( x - 5 ) ( x + 6 ) ( x +4 ) = 0
x = 5
x = -6
x = -4
Intern
Joined: 19 Feb 2006
Posts: 46
Followers: 1

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

Re: squared equations [#permalink]  23 Apr 2006, 07:25
A different approach :

(x^2 - 25)^2 = (x-5)^2

We get 2 equations x^2 - 25 = x-5 and x^2 - 25 = -(x-5)

From 1 we get x^2 -x -20 = (x-5)(x+4)

From 2 we get x^2+x-30 =(x+6)(x-5)

Hence 3 solutions 5,-4 and -6

But my answers are different from yours..ccax
Manager
Joined: 20 Nov 2004
Posts: 108
Followers: 0

Kudos [?]: 3 [0], given: 0

Re: squared equations [#permalink]  23 Apr 2006, 07:30
sherinaparvin wrote:
But my answers are different from yours..ccax

You're right. I swopped the sign for each of the solutions.
Senior Manager
Joined: 08 Jun 2004
Posts: 498
Location: Europe
Followers: 1

Kudos [?]: 39 [0], given: 0

[#permalink]  24 Apr 2006, 04:59

from
x^4 - 51x^2 - 10x + 600 = 0

how you received this one
(x+5)(x+5)(x-4)(x-6) = 0?

And there should be +10x, not -10x.
Intern
Joined: 01 Aug 2006
Posts: 35
Followers: 0

Kudos [?]: 22 [0], given: 0

Re: How many solutions does equation (x^2-25)^2=x^2-10x+25 have [#permalink]  07 Feb 2014, 20:13
(x^2-25)^2=x^2-10x+25
=> |x^2-25|=|x-5|
Case 1: Both +ve or both negative: x^2-25 = x-5 => x^2 - x -20 = 0 => (x-5)(x+4) = 0 => x = 5, -4
Case 2: One +ve and other -ve: x^2-25 = -(x-5) = -x + 5 => x^2 + x -30 = 0 => (x+6)(x-5)= 0 => x = -6, 5

Roots: -6, -4, 5.
Senior Manager
Status: Student
Joined: 26 Aug 2013
Posts: 266
Location: France
Concentration: Finance, General Management
GMAT 1: 650 Q47 V32
GPA: 3.44
Followers: 2

Kudos [?]: 48 [0], given: 401

Re: How many solutions does equation (x^2-25)^2=x^2-10x+25 have [#permalink]  10 Feb 2014, 08:25
The best solution here is to put everything on the same side:

$$(x^2 - 25)^2 = x^2 - 10x + 25$$
$$x^4 - 51x^2 - 10x + 600 = 0$$ => $$(x+5)(x+5)(x-4)(x-6) = 0$$
$$x = - 5$$ or it could be $$x = 4$$ or it could be $$x = 6$$

The answer is 3.

hih
_________________

Think outside the box

Intern
Joined: 25 Sep 2013
Posts: 2
Followers: 0

Kudos [?]: 1 [0], given: 3

Re: How many solutions does equation (x^2-25)^2=x^2-10x+25 have [#permalink]  11 Feb 2014, 11:34
Where am i going wrong? Can someone explain:

Given: (x^2 - 25)^2=x^2-10x+25
=>(x^2 - 25)^2 = (x-5)^2
=>(x^2 - 25) = (x-5)
=>(x^2 - 5^2) = (x-5)
=>(x-5)(x+5) = (x-5)
=>(x+5) = 1
=> x = -4
Just one solution.

Thanks.
Intern
Joined: 19 May 2014
Posts: 31
Followers: 0

Kudos [?]: 10 [0], given: 6

Re: How many solutions does equation (x^2-25)^2=x^2-10x+25 have [#permalink]  22 May 2014, 07:12
LokeshB wrote:
Where am i going wrong? Can someone explain:

Given: (x^2 - 25)^2=x^2-10x+25
=>(x^2 - 25)^2 = (x-5)^2
=>(x^2 - 25) = (x-5)
=>(x^2 - 5^2) = (x-5)
=>(x-5)(x+5) = (x-5)
=>(x+5) = 1
=> x = -4
Just one solution.

Thanks.

Dear Lokesh

You are making a fundamental mistake.

If it's given that $$a^2 = b^2$$
This implies that,$$a = +b$$ or $$a= -b$$

So, in the question above, when you took the square root on both sides, you would get two equations:

$$(x^2 - 25) = (x-5)$$

AND

$$(x^2 - 25) = -(x-5)$$

Hope this helped!
_________________

Please press Kudos if you were helped by my post!

Intern
Joined: 20 May 2014
Posts: 37
Location: India
Schools: IIMC
GMAT 1: 700 Q51 V32
Followers: 0

Kudos [?]: 28 [0], given: 16

Re: How many solutions does equation (x^2-25)^2=x^2-10x+25 have [#permalink]  23 May 2014, 06:43
LokeshB wrote:
Where am i going wrong? Can someone explain:

Given: (x^2 - 25)^2=x^2-10x+25
=>(x^2 - 25)^2 = (x-5)^2
=>(x^2 - 25) = (x-5)
=>(x^2 - 5^2) = (x-5)
=>(x-5)(x+5) = (x-5)
=>(x+5) = 1
=> x = -4
Just one solution.

Thanks.

Hi Lokesh,

You are missing out on the solution of LHS = RHS = 0
Taking x -5 as a root, we get x =5
And putting x = 5 in the equation we get LHS = RHS = 0

Hence, x = 5 is one of the solutions

Golden Rule: Be careful while cancelling out factors involving variables

Rgds,
Rajat
_________________

If you liked the post, please press the'Kudos' button on the left

Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 524
Followers: 96

Kudos [?]: 349 [1] , given: 7

Re: How many solutions does equation (x^2-25)^2=x^2-10x+25 have [#permalink]  23 May 2014, 10:10
1
KUDOS
This is a perfect example of an official GMAT question because it looks complicated but is meant to be solved solely by factoring and using the difference of squares identity. Of course one could expand the entire expression and create a mess, but GMAT writers do not expect students to go in that direction.

See the attached solution in the image.

Cheers,
Dabral
Attachments

GMATClub-05232014.png [ 62 KiB | Viewed 986 times ]

Manager
Joined: 07 Jun 2009
Posts: 212
Followers: 1

Kudos [?]: 30 [0], given: 9

Re: How many solutions does equation (x^2-25)^2=x^2-10x+25 have [#permalink]  12 Jun 2014, 21:55
Solution: 2
x = -4, -6
(x^2-25)^2=x^2-10x+25
{(x+5)(x-5)}^2=(x-5)^2
(x+5)^2 X (x-5)^2=(x-5)^2
(x+5)^2=1
x^2+10x+25=1
x^2+10x+24=0
x=-4,-6
_________________

"Always....Read between the lines"

Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 524
Followers: 96

Kudos [?]: 349 [0], given: 7

Re: How many solutions does equation (x^2-25)^2=x^2-10x+25 have [#permalink]  13 Jun 2014, 07:05
@aknine

{(x+5)(x-5)}^2=(x-5)^2

At this stage, we cannot divide both sides by (x-5)^2, because that would mean ignoring the solution x=5.
Instead, subtract and factor, and that would show that x=5 is also a solution.

Also, once you are at the next stage of
(x+5)^2=1
there is no need expand the (x+5)^2 term, instead we can directly conclude:

x+5 = 1 or x+5=-1
which gives the remaining two solutions of x=4 and x = -6.

Cheers,
Dabral
Re: How many solutions does equation (x^2-25)^2=x^2-10x+25 have   [#permalink] 13 Jun 2014, 07:05
Similar topics Replies Last post
Similar
Topics:
1 Of the three-digit integers greater than 700, how many have two digits 4 07 Sep 2006, 15:31
How many solution set exist for the following set of equatio 2 11 Jan 2014, 19:42
1 Why does equating quadratic coefficients not work here? 1 03 Nov 2012, 06:15
2 How many prime factors does 1000 has? 11 17 Nov 2010, 20:45
How many elements does number set N have? (1) Ten of the 9 26 Jun 2008, 23:29
Display posts from previous: Sort by

# How many solutions does equation (x^2-25)^2=x^2-10x+25 have

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.