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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)
⇒ ๐ฅ2 - 4๐ฅ - 21 = 0
⇒ ๐ฅ2 - 7๐ฅ + 3๐ฅ - 21 = 0
⇒ ๐ฅ(๐ฅ - 7) + 3(๐ฅ - 7) = 0
⇒ (๐ฅ - 7)(๐ฅ + 3) = 0
⇒ ๐ฅ = 7 ๐๐ ๐ฅ = -3 and
If x = -3, x – 4 = -3 - 4 = -7
Hence, required numbers are 3, 7 and -3, -7
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