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
Answer: Option
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.
Please correct and clarify.

Maurya said:   7 years ago
Since all the options are positive we have to choose (1-2a).

Amitabha Das said:   7 years ago
It can also be (2a-1)^2.

G Anirudh said:   7 years ago
Let me help you guys.

Here the given question can have 2 different answers as;

(1-2a)^2 = 4a^2-4a+1= (2a-1)^2.

Hence for questions like these, try to verify with both the answers and select the given option.
here answers are -0.4805 and 1.1039. so since all options are +ve we select the +ve ans i.e. 1.1039.

Sandeep said:   7 years ago
@DIVI.
Answer will be in -ve if you subtracting 0.5195 - 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.

Rahul said:   8 years ago
I do not understand the explanation. Please clarify me.

Harshit said:   8 years ago
Given that a = 0.1039; a<<1; this implies a^2<<<1 and hence it can be ignored int the expression.
So, the value should be approximately equal to 1 - a = 0.8961. The exact value is 0.9393 is also nearly equal to it.

But the option does not contain any matching value. So why should not we consider this question ambiguous?

Jaju said:   8 years ago
Hi @Bhavuk Singh.

How told you to take the square root of - .7922?

Actually, when you take the square root of (2a-1) ^2 it will give you two result either 2a-1 else 1-2a.

You can choose any of the two and yes, two results are possible here. Keeping in mind options given you have to select any one of twos. I think this is clear now?

Bhavuk Singh said:   8 years ago
Given , a = 0.1039
2a - 1= 2(0.1039) - 1 = - .7922.

The square root of a negative number is not a real number. Hence, we use (1 - 2a).


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