Equations

Expert replies

MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Tue Jun 21, 2011 7:10 pm

1. If a^2 + b^2 + 2ab + 2a + 2b = 4, then what is the value of a^2+b^2?
A. 2
B. 3
C. 4
D. 5
E. 6

7. Given an equation x^2 - x + 1 = 0. Find the number of possible values of x?

Like this post

Source: Beat The GMAT — Problem Solving | Tue Jun 21, 2011 7:10 pm

garima99: Master | Next Rank: 500 Posts; Posts: 217; Joined: Tue May 31, 2011 9:42 pmFollowed by: 2 members; Thanked: 8 times

by garima99 » Tue Jun 21, 2011 7:47 pm

MBA.Aspirant wrote:1. If a^2 + b^2 + 2ab + 2a + 2b = 4, then what is the value of a^2+b^2?
A. 2
B. 3
C. 4
D. 5
E. 6

7. Given an equation x^2 - x + 1 = 0. Find the number of possible values of x?

(a+b+1)^2=2^2
so a+b=1 or a+b=-3

Like this post

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Tue Jun 21, 2011 7:51 pm

Hi,
Q1) a^2 + b^2 + 2ab + 2a + 2b = 4. Adding 1 on both sides, we get
a^2 + b^2 + 2ab + 2a + 2b + 1 = 4 + 1
(a+b+1)^2 = 5
(a+b+1) = sqrt5 or -sqrt5
So, a+b = sqrt5 - 1 or -sqrt5 - 1
For different values of a,b we get different values of a^2 + b^2.
Please check the source again. Many questions you have been posting in this section are really not GMAT questions. It is better for you not solve from this source.

Q2) x^2 - x + 1 = 0 => (x - 1/2)^2+3/4 = 0
(x - 1/2)^2 is always greater than or equal to zero. So, (x - 1/2)^2+3/4 >= 3/4
So, it can never be equal to zero.
There are zero possible values of x.

Cheers!

Things are not what they appear to be... nor are they otherwise

Like this post

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Tue Jun 21, 2011 7:54 pm

garima99 wrote: (a+b+1)^2=2^2
so a+b=1 or a+b=-3

Hi,
There is no '1' on LHS. If you have added it you should also add on RHS. Please check that part.

Cheers!

Things are not what they appear to be... nor are they otherwise

Like this post

MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Tue Jun 21, 2011 8:02 pm

Thanks for your reply.

isn't (a+b+1)^2 = a^2 +b^2+1+2ab

that's missing 2a+2b and an extra 1

Like this post

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Tue Jun 21, 2011 8:21 pm

MBA.Aspirant wrote:Thanks for your reply.

isn't (a+b+1)^2 = a^2 +b^2+1+2ab

that's missing 2a+2b and an extra 1

Hi,
(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc +2ca
So, (a+b+1)^2 = a^2 + b^2 + 2ab + 2a + 2b + 1

Cheers!

Things are not what they appear to be... nor are they otherwise

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review