Question

the difference of two natural no is 5 and the difference of their reciprocals is 5/14 find the numbers

Answer 1

Let the two natural numbers be x and y.

A/q

y - x = 5

1/x - 1/y = 5/14

From 1.

y = x + 5

Putting the value of y in eqn. 2

1/x - 1/(x+5) = 5/14

x+5-x / x(x+5) = 5/14

5 / x2 + 5x = 5/14

x2 + 5x - 14 = 0

x2 + (7-2)x - 14 = 0

x2 + 7x - 2x - 14 = 0

x(x+7) - 2(x+7) = 0

(x+7) (x-2) = 0

Either

x+7 = 0

x = -7

Not acceptable because -7 is not a natural number.

Or,

x - 2 = 0

x = 2

so,First number = 2

Other number = (x+5)

2 + 5=7

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Answer 2

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