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Question
The sum of 2 numbers is 18. If the sum of their reciprocals is `1/4` , find the numbers.
Solution
Let these numbers be A and B.
Then as per the question,
A+B= 18, 1/ A + 1/ B= l / 4
⇒ A= 18-B, Putting this in 2nd equation, we get:
⇒ `1/(18 - "B") + 1/"B" = 1/4`
⇒ (B + 18 - B) × 4 = (18 - B) × B
⇒ B2 -18 B + 72 = 0
⇒ B2 -12 B - 6 B + 72 = 0
⇒ B(B-12)- 6(B-12) = 0
⇒ (B-12)(B-6) = 0
⇒ B= 12, 6.
Hence the numbers are 6 and 12.
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