The difference of two natural numbers is 3 and the difference of their reciprocals is . Find the numbers.

Let the natural numbers be ‘a’ and ‘b’.


Given, difference of two natural numbers is 3 and difference of their reciprocals is 3/28


a – b = 3


a = b + 3


and 1/b – 1/a = 3/28


1/b – 1/(b + 3) = 3/28


28(b – b – 3) = -3(b2 + 3b)


b2 + 3b - 28 = 0


b2 + 7b – 4b – 28 = 0


b(b + 7) – 4(b + 7) = 0


(b – 4)(b + 7) = 0


b = 4


Numbers are, 4, 7


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