The difference between the two numbers is 4. If the difference of their reciprocal is , find the numbers.

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7 and 3

7 and -3

-7 and -3

Both A and C

answer is D.

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Detailed Solution

Concept- For now, let's call the two numbers a.
and b The difference between the two numbers is 14, so create an equation out of it. Reciprocal difference is

Then simplify the second equation and use substitution to simplify the equation and find the values of the two numbers.
First, consider two numbers:
and b
Therefore, the reciprocal of these two numbers is 1a.
and 1b. Given that the difference between the two numbers is 14, then:

Now we know that the difference between the reciprocals of the two numbers is

. Here we get:
Question Image

Since I took

Since I thought that

So the reciprocal is the opposite of both numbers i.e.

From this we get ab =21 -(2)
Now replace the value of b.
From equation (2) to equation (1) .
So we get
Question Image

Then apply the zero-coefficient property to determine the value of a. so we get.

So, substitute both values for a. Determine the value of b with equation (2) so we get
Question Image

Hence, the correct answer is option (4) .

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