# Aptitude - Square Root and Cube Root - Discussion

Discussion Forum : Square Root and Cube Root - General Questions (Q.No. 6)
6.

If a = 0.1039, then the value of 4a2 - 4a + 1 + 3a is:

0.1039
0.2078
1.1039
2.1039
Explanation:

4a2 - 4a + 1 + 3a = (1)2 + (2a)2 - 2 x 1 x 2a + 3a

= (1 - 2a)2 + 3a

= (1 - 2a) + 3a

= (1 + a)

= (1 + 0.1039)

= 1.1039

Discussion:
70 comments Page 2 of 7.

Shrikant T. said:   6 years ago
Here you have given the formula (x-y)^2.

If we take the value of x = 2a and value of b = 1 then,
(x-y)^2 = x^2 -2xy + y^2.
i.e 4a^2 - 4a + 1.

But here you have taken (1-2a)^2, which yields the completely different equation.

Your ans is right. But according to KRISHNA ,the sqrt of (2a-1)^2 is +(2a-1) and -(2a-1).so if we choose -(2a-1) then we get

-(2a-1)+3a=-2a+1+3a
=a+1
=.1039+1=1.1039 (ans)

So, this is the technique to SATISFY the option, that has given in the question.

Sorry you are wrong
4*a*a - 4*a + 1 can be written as
4*a*a - 2*a -2*a +1

Taking 2*a common
2*a(2*a-1) -(2*a - 1)

Hence (2*a-1)(2*a-1) but it is given as (1-2*a)(1-2*a) is completely wrong how can he get that ????

If im wrong please explain me ???

After solving we got (2a-1)^2 but according to answer we have to take like this:

(2a-1)^2 = [-1(1-2a)]^2 (take -1 common from (2a-1))

= (-1)^2(1-2a)^2 (here -1*-1=1)

= 1(1-2a)^2

= (1-2a)^2.

Vishal said:   9 years ago
Since the value of a has been given in the question hence 2a-1 can't be square root since then the square root will be negative and options given as answers are positive. Hope you guys got it.

@Latha I have a doubt in your explanation.

You said a=2a, b=1.

While substitute you did(1-2a).

But according to your explanation it is wrong.

Actually it comes(2a-1).

Divi said:   8 years ago
4a^2 - 4a + 1 = (2a - 1)^2
Then square and root cancelld.

2a - 1 + 3a = 5a - 1.
5(0.1039) - 1 = 0.5195 - 1 = 0.4805 is this correct? I it is wrong, anyone explain me.

I do agree with krishan, however 2a-1 is not equal to 1-2a because the value may be the same however, is it postive or negitive value, so can anyone explain on this?

Chinnapa reddy said:   4 years ago
I have one doubt about the solution to the problem why should we take 1-2*a only, there is another chance to take equation as 2*a-1 please tell me a solution.
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