Aptitude - Square Root and Cube Root - Discussion

Is there any other method to solve it?

Not getting how can we take decision at exam time.

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).

4*a*a - 4*a + 1 can also be written as 1 + 4*a*a-4*a can be written as 1 + 4*a*a-2*a-2*a.
1 - 2*a + 4*a*a - 2*a.

Taking 1 as common in first two and 2*a in last two then 1(1 - 2*a)-2*a(1 - 2*a).
Hence (1 - 2*a)(1 - 2*a).

So Both Are Correct. So we have to choose any one of these such it satisfies the options available.

The options are correct and even the answer is correct.

By adopting the formula {a+b} = a^2+2ab+b^2.

Can anyone explain how (1-2a) instead of (2a-1) ?

Guys let me explain this things.
Everyone discuss here is (a-b)^2.

Actually (a-b)^2= (b-a)^2.
For example (5-2)^2=(2-5)^2. Cause square of a negative no is positive.

But you guys know what's wrong in here. The wrong is square root of a no is either positive or negative. In solution taking square root come with +(1-2a) and -(1-2a) so while considering these two we get two answer.

Both of them will satisfy the condition. Hope you guys are get it. Here solution consider only one possibilities of answer.

Let me explain this. When you solve the the equation under the square root, you can have either (2a - 1) or (1 - 2a). According to the question a = 0.1039.

Hence,
2a-1 = 2* 0.1039 -1 which would be negative. You cannot have a negative number inside the square root though.

Hence we have 1 - 2a.

According to the solution we have to follow! that is called reasoning!

@Souji.

(1-2a)² = (2a-1)² = 4a²+1-4a.

So no problem.

@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).