Question

The difference of two number is 4 and their reciporocal 4/21 find numbwr

Answer 1

According to the question

Let the required numbers are x and x - 4,

Given, difference of their reciprocal is 4 / 21

Reciprocal of x = 1 / x  

Reciprocal of x - 4 = 1 / ( x - 4 )  

⇒ Difference of their reciprocal = 4 / 21

$\implies \dfrac{1}{x-4} - \dfrac{1}{x} = \dfrac{4}{21}\\\\\\\implies \dfrac{x-x+4}{x(x-4)} = \dfrac{4}{21}\\\\\\\implies \dfrac{4}{x^2-4x} = \dfrac{4}{21}\\\\\\\implies \dfrac{1}{x^2-4x} =\dfrac{1}{21}\\\\\\\implies x^2 - 4x = 21$

⇒ x^2 - 4x - 21 = 0

⇒ x^2 - ( 7 - 3 )x - 21 = 0

⇒ x^2 - 7x + 3x - 21 = 0

⇒ x( x - 7 ) + 3( x - 7 ) = 0

⇒ ( x - 7 )( x + 3 ) = 0

⇒ x = 7 Or x = - 3

CASE 1 : - When the value of x is 7.

Required numbers are x and ( x - 4 ),

Required numbers are 7 and ( 7 - 4 ) i.e. 3

Required numbers are 7 and 3 .

CASE 2 : - When the value of x is - 3

Required numbers are x and ( x - 4 )

Required numbers are - 3 and ( - 3 - 4 ) i.e. - 7 .

Required numbers are are -3 and -7.

Answer 2

here is your answer OK ☺☺☺☺☺☺☺

let be seeing the denominator the answer is -7 and -3 or +7 and +3. so.....

Let the two numbers be x and y. Then we have two equations :

x - y = 4 … (1)

1/y-1/x=4/21 … (2).......through (2)

x - y = 4xy/21, or

21x - 21y = 4xy …(3). Multiply (1) by 21 to give

21x - 21y = 84 …(1a)

Subtract (1a) and (3) to get

4xy - 84 = 0, or

x = 21/y

equation . (1) so 21/y - y = 4, or

21 - y^2 = 4y, or

y^2 +4y -21 = 0

(y+7)(y-3) = 0
so ☺☺☺☺

Hence Eq.(1), y = -7 and x = -3 or

y = +3 and x = +7.

let check....... ☺☺☺☺☺

Check: x-y = -3-(-7) = 4.

x-y = 7- 3 = 4