SOLUTION: The sum of the reciprocals of two consecutive integers is 11/30. Find these integers.
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Question 151171: The sum of the reciprocals of two consecutive integers is 11/30. Find these integers.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The sum of the reciprocals of two consecutive integers is 11/30. Find these integers.
:
Two consecutive integers: x, (x+1)
:
Sum of reciprocals =
+ =
:
Multiply equation by 30x(x+1) and you have:
30(x+1) + 30x = 11x(x+1)
;
30x + 30 + 30x = 11x^2 + 11x
:
60x + 30 = 11x^2 + 11x
:
0 = 11x^2 + 11x - 60x - 30
a quadratic equation
11x^2 - 49x - 30 = 0
Factors to:
(11x + 6)((x - 5) = 0
The integer solution:
x = 5
:
The two numbers = 5,6
:
Check solution in original equation:
+ =
+ =
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