Equations

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

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.

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.

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

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