SOLUTION: the sum of the reciprocals of two consecutive even intergers is 11/60. Find the integers
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Question 253123: the sum of the reciprocals of two consecutive even intergers is 11/60. Find the 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 even integers is 11/60. Find the integers:
:
two even consecutive integers: x, (x+2)
:
+ =
Multiply by 60x(x+2), results
60(x+2) + 60x = 11x(x+2)
:
60x + 120 + 60x = 11x^2 + 22x
:
Arrange as a quadratic equation
0 = 11x^2 + 22x - 120x - 120
11x^2 - 98x - 120 = 0
:
Were dealing with integers, so it should factor:
(11x + 12) (x - 10) = 0
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Two solutions
x = 10, the integer solution is what we want here
x =
:
The two integers: 10, 12
:
:
Check solution
+ =
+ =
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