Question

The difference of two natural numbers is 3 and the difference of their reciprocals is $\frac{3}{28}$. Find the numbers.

Answer 1

SOLUTION :  

Let one number be x  and other number be x - 3.

Their reciprocals be 1/x & 1/(x - 3)

A.T.Q

1/( x - 3 ) - 1/x = 3/28

[ x - ( x - 3 )]/[ ( x - 3 ) x ] = 3/28

[By taking LCM]

( x - x + 3 )/(x² - 3x ) = 3/28

3/(x² - 3x ) = 3/28

3 × 28 = 3 (x² - 3x)  

[By cross multiplying]

x² - 3x = (28 × 3)/3

x² - 3x = 28

x² - 3x - 28 = 0

x² - 7x + 4x - 28 = 0

[By middle term splitting]

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, so x ≠ - 4

Therefore, x = 7  

Other number = (x - 3) = 7 - 3 = 4  

Hence, the two natural numbers are 4 & 7 .

HOPE THIS  ANSWER WILL HELP YOU….

Answer 2

Step-by-step explanation:

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