SOLUTION: find two consecutive positive odd number given that difference between their reciprocals is 2/63
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Question 256445: find two consecutive positive odd number given that difference between their reciprocals is 2/63
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let 
represent the smaller of the two consecutive odd integers. Then 
must represent the next consecutive odd integer.
The reciprocal of the smaller is then 
, and the reciprocal of the larger one is 
. Then the difference between the reciprocals is:
Combine the fractions in the LHS using the common denominator 
\ -\ x}{x^2\,+\,2x}\ =\ \frac{2}{63})
Collect terms on the left:
Now we have two equal fractions with equal numerators -- therefore the denominators must be equal as well, so:
Solve the factorable quadratic. Discard the negative root. The positive root will be the smaller of the two positive consecutive odd integers.
John
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