Another problem

[krisolaw]

The difference of the reciprocals of two consecutive integers is 1/30. Find the integers.

Please show all steps. I want to check to see if I have figured this one out right. Thanks!

 

[soroban]

Hello, krisolaw!

I prefer to see your work ... then I can tell you if it's correct.

 

[krisolaw]

1/x - 1/(x+1) = 1/30
(x+1)/x(x+1) - x/x(x+1) = 1/30
1/x(x+1) = 1/30
x(x+1) = 30
x^2 + x = 30
x^2 + x - 30 = 0
(x + 6)(x - 5) = 0
x + 6 = 0 or x - 5 = 0
x = -6 or x = 5

If I check with 5 it fits the equation, however the -6 does not. Am I missing something here? Thanks!

 

[pka]

Actually, −6 and 5 both do work

 

[tkhunny]

1/x - 1/(x+1) = 1/30
Am I missing something here?

Right up front, I would have noted that x = 0 and x = -1 are NOT possible answers. Possibly, this knowledge would have encouraged you to try harder on the one you thought didn't work.