Question

The difference of two numbers is 4. If the difference of their reciprocal is $\frac{4}{21}$, find the numbers.

Answer 1

SOLUTION :  

Given : Difference of two numbers is 4.

Let one number be x and the other number be (x + 4).

Their reciprocal are 1/x & 1/(x + 4)

A.T.Q

1/x -1(x+4) = 4/21

(x + 4 - x)/ x(x+4) = 4/21

4/x(x+4) = 4/21

21 × 4 = 4[x(x+4)]

4x² + 16x - 84 = 0

4(x² + 4x - 21) = 0

x² + 4x - 21= 0

x² + 7x - 3x - 21 = 0

[By middle term splitting method]

x(x + 7) - 3(x + 7) = 0

(x - 3) (x + 7) = 0

(x - 3) = 0 or (x + 7) = 0

x = 3  or  x = - 7  

Case 1 :  

When x = 3 , then (x + 4) = 3 + 4 = 7

Case 2 :  

When x = - 7 , then (x + 4) = - 7 + 4 = - 3 .

Hence, the Numbers are (3,7) & (- 3 , - 7) .

HOPE THIS  ANSWER WILL HELP YOU.. ..

Answer 2

Let the one number be x.

Then, other number will be ( x + 4 ).

According to the question,

The difference of their Reciprocal = 1 / x - { 1 / ( x + 4 )} = 4 / 21

( x + 4 - x ) / ( x + 4 ) x = 4 / 21

4 / ( x^2 + 4x ) = 4 / 21

21 × 4 = 4x^2 + 16x

84 = 4x^2 + 16x

0 = 4x^2 + 16x - 84

0 = 4 ( x^2 + 4x - 21 )

0 = x^2 + 7x - 3x - 21

0 = x ( x + 7 ) - 3 ( x + 7 )

0 = ( x - 3 ) ( x + 7 )

x = 3, - 7

$<h3>So, One number is x = 3$

Other number is ( x + 4 ) = ( 3 + 4 ) = 7