Last visit was: 22 Apr 2026, 23:05 It is currently 22 Apr 2026, 23:05
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
HIMALAYA
User avatar
Joined: 05 Apr 2005
Last visit: 09 Aug 2011
Posts: 796
Own Kudos:
270
Posts: 796
Kudos: 270
if x+(1/x) = 5, what is x^2+(1/x^2) 24 Oct 2005, 19:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions

History

Date
Time
Result
Not Attempted Yet
if x+(1/x) = 5, what is x^2+(1/x^2)?



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
vikramm
User avatar
Joined: 30 Oct 2004
Last visit: 28 Nov 2006
Posts: 156
Own Kudos:
254
Posts: 156
Kudos: 254
if x+(1/x) = 5, what is x^2+(1/x^2) 24 Oct 2005, 19:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
x + (1/x) = 5

x^2 + (1/x^2) = (x + 1/x)^2 - 2 = 5^2-2 = 25-2 = 23
User avatar
mbaqst
User avatar
Joined: 17 Sep 2005
Last visit: 04 Nov 2005
Posts: 22
Own Kudos:
15
Location: California
Posts: 22
Kudos: 15
if x+(1/x) = 5, what is x^2+(1/x^2) 24 Oct 2005, 20:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
23

Given x + 1/x = 5; Square on both sides..

(x + 1/x)^2 = 5^2
x^2 + 1/x^2 + 2*x*1/x = 25
x^2 + 1/x^2 + 2 = 25
x^2 + 1/x^2 = 25 - 2
x^2 + 1/x^2 = 23
User avatar
BumblebeeMan
User avatar
Joined: 05 Oct 2005
Last visit: 23 Jun 2009
Posts: 39
Own Kudos:
5
Posts: 39
Kudos: 5
if x+(1/x) = 5, what is x^2+(1/x^2) 24 Oct 2005, 20:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
vikramm
x + (1/x) = 5

x^2 + (1/x^2) = (x + 1/x)^2 - 2 = 5^2-2 = 25-2 = 23
Show more


Vikram, I agree with your answer, but I'm not sure what steps you took to get there. It looks like you're taking x^2 + (1/x^2) and making that equal to (x + 1/x)^2 (although I'm not sure where the -2 is coming from).
But, (x+1/x)^2 really works out to x^2 + 2/x + 1/x^4.
Could you explain your methods?

Here's how I came up with the answer:

x + (1/x) = 5, so 1/x = 5-x
also, if you multiply both side of the first equation by x, you get:
x^2 + 1 = 5x
x^2 = 5x-1

Plug the value for 1/x into the second equation:

x^2 + (5-x)^2 = x^2 + 25 - 10x + x^2
=2x^2 - 10x + 25

Then, plug the value for x^2 = 5x-1 into this last equation:
2(5x-1) - 10x + 25
=10x -2 - 10x + 25
= -2 + 25
= 23

UPDATED
D'oh, I see the dumb mistake I made now. My method, while it works, is unnecessarily long. Thanks to both of you who provided the shorter explanation.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderator:
Bunuel
Math Expert
109763 posts