Question

the difference of two natural number is 3 and the difference of their reciprocals is 3/28. find the number

Answer 1

Let the nos be X and X+3.
Their reciprocals are 1/X and 1/X+3.
Now 1/X-1/X-3=3/28.
So, X+3-X/X^2+3X = 3/28.
3*28=3X^2+9X.
84=3X^2+9X.
3X^2+9X-84=0 /3
X^2+3X-28=0
(X+7)(X-4)=0
Now
X=-7 or X=+4.
Case-1
X=-7
X+3=-7+3=-4
Now
-4-(-7)=-4+7=+3.
Case-2
X=+4
X+3=4+3=7
Now
7-4=+3.
Therefore the nos are 7 and 4.

Answer 2

Answer:

According to the question,

Let the required two numbers are x and ( x - 3 ),

Given, the difference of their reciprocals is 3 / 28.

Reciprocal of x = 1 / x

Reciprocal of x - 3 = 1 / ( x - 3 )

⇒ Difference = 3 / 28

⇒ x^2 - 3x - 28 = 0

⇒ x^2 - ( 7 - 4 )x - 28 = 0

⇒ x^2 - 7x + 4x - 28 = 0

⇒ x( x - 7 ) + 4( x - 7 ) = 0

⇒ ( x - 7 )( x + 4 ) = 0

⇒ x = 7 or - 4

Given that the required numbers are natural numbers, so they can't be negative.

∴ x = 7

Other number = x - 3 = 7 - 3 = 4

Therefore, required natural numbers are 7 and 4 .