SOLUTION: Find two consecutive integers such that the sum of their reciprocals is 7/24

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Question 294568: Find two consecutive integers such that the sum of their reciprocals is 7/24
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find two consecutive integers such that the sum of their reciprocals is 7/24
:
Two consecutive integers: x, (x+1)
:
1%2Fx + 1%2F%28%28x%2B1%29%29 = 7%2F24
Multiply by 24x(x+1), results
24(x+1) + 24x = 7x(x+1)
:
24x + 24 + 24x = 7x^2 + 7x
:
48x + 24 = 7x^2 + 7x
:
0 = 7x^2 + 7x - 48x - 24
:
7x^2 - 41x - 24 = 0
Will not factor, so don't think there is an integer solution