Aptitude - Decimal Fraction - Discussion

Thanks @Tushar.

We know that.

(a + b) ^2 = a^2 + b^2 + 2ab.

Here a = 11.98.

b = 0.02.

2ab = 11.98x.

Therefore,

x = 2ab/11.98.

= (2*11.98*0.02) / 11.98 (11.98 cancel each other).

= 2*0.02.

x = 0.04.

Here in given question (11.98)^2 (11.98*x)+(0.02)^2---- (1).

Then it is like as (x+y)2 = x2+2xy+y2---- (2).

Then compare it (1) & (2).

x = 11.98 and y = 0.02 and 2.x.y = 11.98*x.

Here x = 2*0.02 because in that question there is missed the 'y' and 2.

That will is present in that "X" position that question will be converted into perfect square like (11.98+0.02) ^2.

In "x " place the 2*0.02 will be written.

How 11.98*x = 2*11.98*0.02 is equal?

How we can write as this : 11.98*x = 2*11.98*0.02.

Is there is any formula?

For better understanding
We know for perfect square we need x*x or y*y.
e.g. 3*3=9 is a perfect square

and given is :(11.98*11.98 + 0.02*0.02 + 11.98*x)
will be a perfect square if 11.98 x x = 2 x 11.98 x 0.02
this is according to formula (x+y)2 i.e. (x+y)2 = x2+y2+2xy
we have x2and y2 we need 2xy = 2 x 11.98 x 0.02
therefore 11.98 x x = 2 x 11.98 x 0.02
and thus x comes out to be x = 0.04

Please describe whole calculation.