Question

4.
16. The difference of two numbers is 4. If the difference of their reciprocals is4/21
​

Answer 1

Answer:

The two numbers are 3 and 7.

Step-by-step explanation:

Let the two numbers be x and x-4.

As per the gven information

The difference in their reciprocal is 4/21

$\frac{1}{x - 4} - \frac{1}{x} = \frac{4}{21}$

$\frac{x - x + 4 }{ {x}^{2} - 4x } = \frac{4}{21}$

$\frac{ 4}{ {x}^{2} - 4x } = \frac{4}{21}$

$4 \times 21 = 4 \times ( {x}^{2} - 4x)$

$21 = {x}^{2} - 4x$

${x}^{2} - 4x - 21 = 0$

${x}^{2} - 7x + 3x - 21 = 0$

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

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

Either x - 7 = 0 or, x + 3 = 0

=> x = 7 or, x = - 3

Reject x = -3

The two numbers are 3 and 7.