The sum of the reciprocals of two consecutive even integers is 7/24. Write an equation that can be used to find the two integers. Find the two integers.

Let the numbers be x and (x + 2) so we have

1/x + 1 / (x + 2) = 7 / 24

Multiply through by 24 x (x+2) : -

24 (x+2) + 24x = 7x (x+2)

24x + 48 + 24x = 7x^2 + 14

7x^2 - 48x - 34 = 0

this hasn't got integer roots

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