1.

The difference of two natural number is 3 and the difference of their reciprocal is 3/28. Find the numbers.

Answer» HI ,

Let x , x - 3 are TWO numbers .

according to the problem given ,

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

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

( x - x + 3 )/(x² - 3x ) = 3/28

3/(x² - 3x ) = 3/28

( x² - 3x ) /3 = 28/3

x² - 3x = 28

x² - 3x - 28 = 0

x² - 7x + 4x - 28 = 0

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

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

Therefore ,

x - 7 = 0 or x + 4 = 0

x = 7 or x = - 4

Required numbers are;,

1 ) if x = 7 ,

x - 3 = 7 - 3 = 4

( 7 , 4 )

2 ) if x = - 4 ,

x - 3 = -4 - 3 = -7

( - 4 , - 7 )

I hope this HELPS you.

: )


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