The difference of the reciprocals of two consecutive integers is 1/72. What are the two integers?
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Let two consecutive integers be x and (x+1)
Therefore from the question ,
1/x -1/(x+1) = 1/72
By taking LCM ,
x^2 + x -72 = 0
So solving this quadratic eq ,
We get
x = 8 , -9 (neglect)
Second integer = x +1 = 8+1 = 9
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