Question 269624
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.