# 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 4*a*^{2} - 4*a* + 1 + 3*a* is:

Answer: Option

Explanation:

4*a*^{2} - 4*a* + 1 + 3*a*
= (1)^{2} + (2*a*)^{2} - 2 x 1 x 2*a* + 3*a*

= (1 - 2*a*)^{2} + 3*a*

= (1 - 2*a*) + 3*a*

= (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.

Please correct and clarify.

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.

Please correct and clarify.

Sudarsan said:
1 decade ago

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.

-(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.

Krishna said:
1 decade ago

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 ???

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 ???

Manju said:
1 decade ago

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.

(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.

Souji said:
1 decade ago

@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).

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.

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.

Rakesh. said:
1 decade ago

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.

(1)

Sid said:
1 decade ago

Who goes for the answer anyone solving this would go for the formula asq - 2ab + bsq which will give (2a - 1)sq.

I don't think (1-2a)sq can be the way out.

I don't think (1-2a)sq can be the way out.

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