SOLUTION: The difference of the reciprocals of two consecutive integers is 1/42. Find the integers.

Question 269624: The difference of the reciprocals of two consecutive integers is 1/42. Find the integers.
Found 2 solutions by stanbon, drk:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The difference of the reciprocals of two consecutive integers is 1/42. Find the integers.
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1st: x
2nd: x+1
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Equation:
1/x - 1/(x+1) = 1/42
[(x+1) - x]/[x(x+1)] = 1/42
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1/(x^2+x) = 1/42
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x^2+x = 42
x^2 + x -42 = 0
Factor:
(x+7)(x-6) = 0
x = -7 or x = 6
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If x = -7, x+1 = -6
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If x = 6, x+1 = 7
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Cheers,
Stan H.
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
we have
(i)
simplify the left side to get
(ii)
cross multiply to get
(iii)
set = 0 to get
(iv)
factoring, we get
(v)
So, x = -7 or x = 6
If x = -7 then x + 1 = -6 and we get -1/7 - (-1/6) = -1/7 + 1/6 = 1/42
If x = 6 then x + 1 = 7 and we get 1/6 - 1/7 = 1/42
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