Question

the difference of two number is 4 if the difference of their reciprocal is 4 by 21 find the two numbers

Answer 1

Here, As per the question,

Let one number be x.

Another number = x+4.

Now,

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

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

4x^2+16x -84= 0

x^2+4x -21= 0

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

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

So, x =3

Thus, Numbers are 3 and 7.

Hope you will find it helpful

Answer 2

$<b> <i> Hlo frnd!!!!$
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Given that the difference of two numbers is 4

Let the two numbers be a & (a-4)

Acc.To statement :

$\frac{1}{a - 4} - \frac{1}{a} = \frac{4}{21} \\ \\ \frac{a - a + 4}{a(a - 4)} = \frac{4}{21} \\ \\ \frac{4}{ {a}^{2} - 4a } = \frac{4}{21} \\ \\ 84 = 4a {}^{2} - 16a \\ \\ 84 = 4(a {}^{2} - 4a) \\ \\ 21 = {a}^{2} - 4a \\ \\ {a}^{2} - 4a - 21 = 0 \\ \\ {a }^{2} - 7a + 3a - 21 \\ \\ a(a - 7) + 3(a - 7) \\ \\ (a - 7)(a + 3) = 0 \\ \\ a = 7$

SO , The first number is 7

and the another number is 3
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HOPE IT HELPS UH ✌