The difference of two natural number is 3 and the difference of their reciprocal is 3/28. Find the numbers.
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Answered by
25
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.
: )
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.
: )
PQRXTZ:
if one no. is x and difference between 2 no.is 3 then how other number will become x-3
Sorry u are correct .....I have not seen it properly
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12
Refers to attachment....!!!
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