Question

the difference of two numbers is 4and the difference of their reciprocal is 4/21. find the numbers

Answer 1

Let the first number be a

Second number = a - 4

According to question,

1/a - 1/(a-4) = 4 /21

=> [ a - 4 - a] / a (a - 4)= 4 / 21

=> ( - 4) / (a^2 - 4a) =4 /21

=> 21 (-4) = 4a^2 - 16a

=> - 84 = 4a^2 - 16a

=> 4a^2 - 16a + 84 = 0

=> a^2 - 4a + 21 = 0

=> a^2 - 7a - 3a + 21 = 0

=> a( a - 7) - 3(a - 7) = 0

=> (a - 7)(a - 3) = 0

First number = 7

Second number = 3

Answer 2

The correct answer for your question is seven and three.

Your Question:

The difference of two numbers is 4.if the difference of their reciprocals is 4/21,find the numbers

So, the difference of the two unknown numbers is 4.

X - Y = 4 ------→ (1)

Here the reciprocal of X = 1/X

Here the reciprocal of Y = 1/Y

The difference of the reciprocals is 4/21

21Y - 21X = 4XY ------→ (2)

From the Equation (1)

X – Y = 4

X = 4 + Y ------→ (3)

Combining the equation (2) and (3) we get.

Y = 12/4  

Y = 3

Substituting the Y in equation (1) we get

X = 4+3

X = 7

Hence the two unknown number are 7 and 3.