Last visit was: 26 Dec 2024, 11:47 It is currently 26 Dec 2024, 11:47
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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 GRE 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
PREVIOUS TOPIC
NEXT TOPIC

If a + 1/a = 4 then what is the value of a^2 + 1/a^2 ?

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30511
Own Kudos [?]: 36867 [1]
Given Kudos: 26109
Send PM
If a + 1/a = 4 then what is the value of a^2 + 1/a^2 ? [#permalink] New post   05 Jun 2022, 14:19
1
Expert Reply
00:00

Question Stats:

57% (00:54) correct 42% (01:24) wrong based on 14 sessions

Hide Show timer Statistics

If \(a + \frac{1}{a} = 4\) then what is the value of \(a^2 + \frac{1}{a^2}\) ?

A. 12
B. 14
C. 16
D. 18
E. 20

ShowHide Answer
Official Answer
B
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12238 [0]
Given Kudos: 136
Send PM

Top Member of the Month
Re: If a + 1/a = 4 then what is the value of a^2 + 1/a^2 ? [#permalink] New post   05 Jun 2022, 16:38
Carcass wrote:
If \(a + \frac{1}{a} = 4\) then what is the value of \(a^2 + \frac{1}{a^2}\) ?

A. 12
B. 14
C. 16
D. 18
E. 20


Strategy: When I compare the two given expressions, I recognize that \(a^2\) is the square of \(a\), and \(\frac{1}{a^2}\) is the square of \(\frac{1}{a}\).
So, let's see what happens if we take the given equation, \(a + \frac{1}{a} = 4\), and square both sides.

We get: \((a + \frac{1}{a})^2 = 4^2\)

Use FOIL to expand the left side: \(a^2 + 1 + 1 + \frac{1}{a^2} = 16\)

Simplify: \(a^2 + 2 + \frac{1}{a^2} = 16\)

Subtract \(2\) from both sides of the equation: \(a^2 + \frac{1}{a^2} = 14\)

Answer: B
Prep Club for GRE Bot
gmatclubot
Re: If a + 1/a = 4 then what is the value of a^2 + 1/a^2 ? [#permalink]
05 Jun 2022, 16:38
Moderators:
adewale223
GRE Instructor
88 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1115 posts
VibhuAnurag
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact