Aptitude - Decimal Fraction - Discussion
Discussion Forum : Decimal Fraction - General Questions (Q.No. 8)
8.
The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to:
Answer: Option
Explanation:
Given expression = (11.98)2 + (0.02)2 + 11.98 x x.
For the given expression to be a perfect square, we must have
11.98 x x = 2 x 11.98 x 0.02 or x = 0.04
Discussion:
27 comments Page 1 of 3.
Ram said:
1 decade ago
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.
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.
Tushar said:
1 decade ago
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
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
JSubba said:
7 years ago
Simple explanation.
For it to be a perfect square it should be like this: a^2 + 2ab + b^2 So what's missing in that equation to be a perfect square is 2b so here b is 0.02 so 2*0.02 = 0.04.
For it to be a perfect square it should be like this: a^2 + 2ab + b^2 So what's missing in that equation to be a perfect square is 2b so here b is 0.02 so 2*0.02 = 0.04.
(6)
Nandaraj said:
1 decade ago
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.
(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.
(28)
Vanaja said:
1 year ago
=> (11.98)^2 + (0.02)^2 + 11.98 * x.
=>11.98*x = 2 * 11.98 * 0.02.
=>11.98*x = 0.04 * 11.98.
X = 0.04 * 11.98/11.98.
X = 0.04.
=>11.98*x = 2 * 11.98 * 0.02.
=>11.98*x = 0.04 * 11.98.
X = 0.04 * 11.98/11.98.
X = 0.04.
(8)
Shweta said:
5 years ago
I think the ans should be 0.2.
(11.98)^2+2*11.98*0.02 +(0.02)^2.
2*0.02= 0.04=x^2.
x=0.2.
(11.98)^2+2*11.98*0.02 +(0.02)^2.
2*0.02= 0.04=x^2.
x=0.2.
(3)
Kajal said:
7 years ago
Here, it is given as 11.98 xx.
Then why did u take 2ab=11.98x? Please explain it.
Then why did u take 2ab=11.98x? Please explain it.
Dipika said:
1 decade ago
How we can write as this : 11.98*x = 2*11.98*0.02.
Is there is any formula?
Is there is any formula?
Sachin said:
3 years ago
@Nandaraj.
If we take b= 0. 2 then x = 0. 4, that will also be an answer.
If we take b= 0. 2 then x = 0. 4, that will also be an answer.
(4)
Ssundaram said:
8 years ago
Thanks for the detailed explanation @Tushar, @Ram, @Nandaraj.
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