Last visit was: 10 Jul 2025, 04:03 It is currently 10 Jul 2025, 04:03
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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
Back to Forum
Create Topic
605-655 Level|   Algebra|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 Jul 2025
Posts: 102,612
Own Kudos:
740,012
Given Kudos: 98,069
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,612
Kudos: 740,012
If a = 1/(2^(1/2) - 1) - 2, what is a^2 + 2a + 4? 29 Mar 2023, 07:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

68% (02:07) correct 32% (02:39) wrong based on 93 sessions

History

Date
Time
Result
Not Attempted Yet
If \(a = \frac{1}{\sqrt{2}-1}-2,\) what is \(a^2 + 2a + 4\)?

A. \(2\)

B. \(3\)

C. \(4\)

D. \(5\)

E. \(6\)
ShowHide Answer
Official Answer
D
User avatar
gmatophobia
User avatar
Quant Chat Moderator
Joined: 22 Dec 2016
Last visit: 09 Jul 2025
Posts: 3,149
Own Kudos:
8,946
Given Kudos: 1,860
Location: India
Concentration: Strategy, Leadership
Products:
GMAT Club Tests
Posts: 3,149
Kudos: 8,946
If a = 1/(2^(1/2) - 1) - 2, what is a^2 + 2a + 4? 29 Mar 2023, 11:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If \(a = \frac{1}{\sqrt{2}-1}-2,\) what is \(a^2 + 2a + 4\)?

A. \(2\)

B. \(3\)

C. \(4\)

D. \(5\)

E. \(6\)

Not sure what am I doing wrong here -

\(a = \frac{1}{\sqrt{2}-1}-2\)

\(a = \frac{1* (\sqrt{2}+1)}{(\sqrt{2}-1) (\sqrt{2}+1)}-2\)

\(a = \frac{1* (\sqrt{2}+1)}{2-1}-2\)

\(a = (\sqrt{2}+1) -2\)

\(a + 2= (\sqrt{2}+1) -2 + 2\)

\((a + 2)^2= (\sqrt{2}+1)^2\)

\(a^2 + 2a + 4= 3 + 2\sqrt{2}\)

:dontknow:
User avatar
Nabneet
User avatar
Joined: 27 Dec 2022
Last visit: 19 Aug 2024
Posts: 105
Own Kudos:
106
Given Kudos: 40
Location: India
GMAT 1: 550 Q47 V20
WE:Other (Other)
GMAT 1: 550 Q47 V20
Posts: 105
Kudos: 106
If a = 1/(2^(1/2) - 1) - 2, what is a^2 + 2a + 4? 30 Mar 2023, 08:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatophobia
Bunuel
If \(a = \frac{1}{\sqrt{2}-1}-2,\) what is \(a^2 + 2a + 4\)?

A. \(2\)

B. \(3\)

C. \(4\)

D. \(5\)

E. \(6\)

Not sure what am I doing wrong here -

\(a = \frac{1}{\sqrt{2}-1}-2\)

\(a = \frac{1* (\sqrt{2}+1)}{(\sqrt{2}-1) (\sqrt{2}+1)}-2\)

\(a = \frac{1* (\sqrt{2}+1)}{2-1}-2\)

\(a = (\sqrt{2}+1) -2\)

\(a + 2= (\sqrt{2}+1) -2 + 2\)

\((a + 2)^2= (\sqrt{2}+1)^2\)

\(a^2 + 2a + 4= 3 + 2\sqrt{2}\)

:dontknow:

a has two parts , u just cannot simplify one part of it. Its wrong
If u want to simplify then make it a single value and then u can multiply in num. & deno.

take example,
a= (1/root 2) - 2

is it same as the value , (root2/2) -2 ?



Solution:

a^2 + 2a + 4 = (a+2)^2 -2a

put the value of a in the eqn and solve

Answer we will get is 5.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 Jul 2025
Posts: 102,612
Own Kudos:
740,012
 [2]
Given Kudos: 98,069
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,612
Kudos: 740,012
 [2]
If a = 1/(2^(1/2) - 1) - 2, what is a^2 + 2a + 4? 30 Mar 2023, 08:48
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
gmatophobia
Bunuel
If \(a = \frac{1}{\sqrt{2}-1}-2,\) what is \(a^2 + 2a + 4\)?

A. \(2\)

B. \(3\)

C. \(4\)

D. \(5\)

E. \(6\)

Not sure what am I doing wrong here -

\(a = \frac{1}{\sqrt{2}-1}-2\)

\(a = \frac{1* (\sqrt{2}+1)}{(\sqrt{2}-1) (\sqrt{2}+1)}-2\)

\(a = \frac{1* (\sqrt{2}+1)}{2-1}-2\)

\(a = (\sqrt{2}+1) -2\)

\(a + 2= (\sqrt{2}+1) -2 + 2\)

\((a + 2)^2= (\sqrt{2}+1)^2\)

\(a^2 + 2a + 4= 3 + 2\sqrt{2}\)

:dontknow:

\(a = \frac{1}{\sqrt{2}-1}-2= \frac{\sqrt{2}+1}{(\sqrt{2}-1)(\sqrt{2}+1)}-2=\frac{\sqrt{2}+1}{2-1}-2=(\sqrt{2}+1)-2=\sqrt{2}-1\).

\(a^2 + 2a + 4=(a+1)^2 + 3= (\sqrt{2}-1 + 1)^2+3=2+3=5\).

Answer: D.
User avatar
gmatophobia
User avatar
Quant Chat Moderator
Joined: 22 Dec 2016
Last visit: 09 Jul 2025
Posts: 3,149
Own Kudos:
8,946
Given Kudos: 1,860
Location: India
Concentration: Strategy, Leadership
Products:
GMAT Club Tests
Posts: 3,149
Kudos: 8,946
If a = 1/(2^(1/2) - 1) - 2, what is a^2 + 2a + 4? 30 Mar 2023, 08:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Nabneet

a has two parts , u just cannot simplify one part of it. Its wrong
If u want to simplify then make it a single value and then u can multiply in num. & deno.

take example,
a= (1/root 2) - 2

is it same as the value , (root2/2) -2 ?



Solution:

a^2 + 2a + 4 = (a+2)^2 -2a

put the value of a in the eqn and solve

Answer we will get is 5.

Thanks for your reply Nabneet.

While I tried to grasp the part in which you mentioned that the rationalization part was incorrect I couldn't follow it completely. My apologies for the same.

With respect to the example provided in the explanation, let me work that here with you -

Quote:
take example,
a= (1/root 2) - 2

is it same as the value , (root2/2) -2 ?

\(a = \frac{1}{\sqrt{2}} - 2 \)

By PEDMAS rule, we first solve \(\frac{1}{\sqrt{2}}\) = \(\frac{1}{1.41421356237}\)

\(a = 0.70710678118 - 2 \) = -1.29289321881

\(a = \frac{\sqrt{2}}{2} - 2 \)

By PEDMAS rule, we first solve \(\frac{\sqrt{2}}{2}\) = \(\frac{1.41421356237}{2}\)

\(a = 0.70710678118 - 2 \) = -1.29289321881

Aren't they the same :think:
User avatar
gmatophobia
User avatar
Quant Chat Moderator
Joined: 22 Dec 2016
Last visit: 09 Jul 2025
Posts: 3,149
Own Kudos:
8,946
Given Kudos: 1,860
Location: India
Concentration: Strategy, Leadership
Products:
GMAT Club Tests
Posts: 3,149
Kudos: 8,946
If a = 1/(2^(1/2) - 1) - 2, what is a^2 + 2a + 4? 30 Mar 2023, 09:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
gmatophobia
Bunuel
If \(a = \frac{1}{\sqrt{2}-1}-2,\) what is \(a^2 + 2a + 4\)?

A. \(2\)

B. \(3\)

C. \(4\)

D. \(5\)

E. \(6\)

Not sure what am I doing wrong here -

\(a = \frac{1}{\sqrt{2}-1}-2\)

\(a = \frac{1* (\sqrt{2}+1)}{(\sqrt{2}-1) (\sqrt{2}+1)}-2\)

\(a = \frac{1* (\sqrt{2}+1)}{2-1}-2\)

\(a = (\sqrt{2}+1) -2\)

\(a + 2= (\sqrt{2}+1) -2 + 2\)

\((a + 2)^2= (\sqrt{2}+1)^2\)

\(a^2 + 2a + 4= 3 + 2\sqrt{2}\)

:dontknow:

\(a = \frac{1}{\sqrt{2}-1}-2= \frac{\sqrt{2}+1}{(\sqrt{2}-1)(\sqrt{2}+1)}-2=\frac{\sqrt{2}+1}{2-1}-2=(\sqrt{2}+1)-2=\sqrt{2}-1\).

\(a^2 + 2a + 4=(a+1)^2 + 3= (\sqrt{2}-1 + 1)^2+3=2+3=5\).

Answer: D.

:facepalm_man:

I messed up \((a+2)^2\) - Where should I go and hide :cry:

Thanks Bunuel :)
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 Jul 2025
Posts: 102,612
Own Kudos:
740,012
 [1]
Given Kudos: 98,069
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,612
Kudos: 740,012
 [1]
If a = 1/(2^(1/2) - 1) - 2, what is a^2 + 2a + 4? 30 Mar 2023, 09:07
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatophobia
:facepalm_man:

I messed up \((a+2)^2\) - Where should I go and hide :cry:

Thanks Bunuel :)

Errare humanum est. It happens to the best of us.
Moderators:
Bunuel
Math Expert
102612 posts
Krunaal
PS Forum Moderator
683 posts