Question 860872
find two positive integers that differ by 8 and whose reciprocal differ by 1/6. 
-------
Equations:
x - y = 8
(1/x) - (1/y) = 1/6
----------
Modify:
x = y + 8
---------
Substitute:
(1/(y+8)) - 1/y = 1/6
-------
Multiply thru by 6y(y+8)
6y - 6(y+8) = y(y+8)
-------
y^2 + 8y + 48 = 0
This quadratic has no integer roots.
-------------------------------------
Cheers,
Stan H.