Q. 275.0( 3 Votes )

The difference of

Answer :

Let the larger natural number be x and the smaller natural number be y.


Given, x – y = 3 … (1)


And … [ If x > y, then 1/x < 1/y]



From (1),



Cross multiplying, we get


84 = 3xy


y = 28/x … (2)


Substituting (2) in (1),


x – 28/x = 3


(x2 – 28)/x = 3


x2 – 28 = 3x


x2 – 3x – 28 = 0


By factorization method,


x2 + 7x - 4x – 28 = 0


x (x + 7) - 4 (x + 7) = 0


(x + 7) (x - 4) = 0


x + 7 = 0 (or) x - 4 = 0


x = -7 (or) x = 4


Since, x is a natural number, x = 4.


Putting the above x value in (2), we get


y = 28/4


y = 7


i.e. x, y = 4, 7


The numbers are 4, 7.


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