Question
Fri November 30, 2012 By:
 

the sum of reciprocals of two consecutive numbers is 13/132 find the numbers.

Expert Reply
Sat December 01, 2012
Let the number be X & X+1
1/X+1/(X+1)=13/132
or, taking LCM
 
(X+1+X)/(X^2+X)=13/132
Cross multiplying
132+264X=13X^2+13X
or, 13X^2-251X-132=0
 
this equation does not have ingral roots as the discriminant is not a perfect square ther such a condition is not possible .
 
 
NOTE: If in place of 13/132 it is 23/132 then the numbers will be 12 &13.
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