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# The Difference of Two Numbers is 4. If the Difference of Their Reciprocals is 4/21. Find the Numbers. - Mathematics

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#### Question

The difference of two numbers is 4. If the difference of their reciprocals is 4/21. Find the numbers.

#### Solution

Let the two numbers be x and x - 4

Given that the difference of two numbers is 4.

By the given hypothesis, we have

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

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

⇒ 84 = 4x(x – 4)

⇒ 𝑥2 - 4𝑥 - 21 = 0

⇒ 𝑥2 - 7𝑥 + 3𝑥 - 21 = 0

⇒ 𝑥(𝑥 - 7) + 3(𝑥 - 7) = 0

⇒ (𝑥 - 7)(𝑥 + 3) = 0

⇒ 𝑥 = 7 𝑜𝑟 𝑥 = -3 and

If x = -3, x – 4 = -3 - 4 = -7

Hence, required numbers are 3, 7 and -3, -7

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