SOLUTION: The sum of a rational number (fraction) and its reciprocal is equal to some positive integer plus 69/110. What is the integer? choose the answer and explain the reason to choose yo

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Question 479892: The sum of a rational number (fraction) and its reciprocal is equal to some positive integer plus 69/110. What is the integer? choose the answer and explain the reason to choose your response
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Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
No one seems to want this problem and I am not too happy with this effort but here it is:
:
Let x = the rational number
Let y = "some positive integer"
:
The sum of a rational number (fraction) and its reciprocal is equal to some positive integer plus 69/110.
x + 1%2Fx = y + 69%2F110
Only y = 4, seems to work out for me here
x + 1%2Fx = 4 + 69%2F110
x + 1%2Fx = 440%2F110 + 69%2F110
x + 1%2Fx = 509%2F110
Find x
x + 1%2Fx -509%2F110 = 0
Multiply by 110x
110x^2 - 509x + 110 = 0
Using the quadratic formula: a=110, b=-509, c=110
One solution that works x = 4.4 which is 44%2F10 so we have:
44%2F10 + 10%2F44 = 4 + 69%2F110
Checking it
968%2F220 + 50%2F220%29+=+%7B%7B%7B880%2F220 + 138%2F220
1018%2F220 = 1018%2F220