SOLUTION: the sum of the reciprocals of two consecutive even integers is 9/40. what are the integers?

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Question 789858: the sum of the reciprocals of two consecutive even integers is 9/40. what are the integers?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let the integers be x & x+2
1/x + 1/(x+2) =9/40
multiply equation by 40x(x+2)
40(x+2)+40x=9x(x+2)
40x+80+40x=9x^2+18x
9x^2+18x-80x-80=0
9x^2-62x-80=0
solve by quadratic formula
a= 9 , b= -62 , c= -80

b^2-4ac= 3844 + 2880
b^2-4ac= 6724
%09sqrt%28%096724%09%29=%0982%09
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 62 + 82 )/ 18
x1= 8.00
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 62 -82 ) / 18
x2= -1.11
8 is an integer
so the integers are 8 & 10