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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: How many solutions does equation (x^2-25)^2=x^2-10x+25 have [#permalink]

Show Tags

07 Feb 2014, 21:13

(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

Re: How many solutions does equation (x^2-25)^2=x^2-10x+25 have [#permalink]

Show Tags

10 Feb 2014, 09:25

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 \(x = 6\)

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 1685 times ]

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.

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...