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The difference of two numbers is 4. If the difference of their reciprocals is 4/21. Find the numbers.
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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)
⇒ ЁЭСе2 - 4ЁЭСе - 21 = 0
⇒ ЁЭСе2 - 7ЁЭСе + 3ЁЭСе - 21 = 0
⇒ ЁЭСе(ЁЭСе - 7) + 3(ЁЭСе - 7) = 0
⇒ (ЁЭСе - 7)(ЁЭСе + 3) = 0
⇒ ЁЭСе = 7 ЁЭСЬЁЭСЯ ЁЭСе = -3 and
If x = -3, x – 4 = -3 - 4 = -7
Hence, required numbers are 3, 7 and -3, -7
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