SOLUTION: If the twice the reciprocal of the larger of two consecutive integers is subtracted from the reciprocal of the smaller, the result is -5 times the reciprocal of the product of the

Question 377485: If the twice the reciprocal of the larger of two consecutive integers is subtracted from the reciprocal of the smaller, the result is -5 times the reciprocal of the product of the two integers. Find the integers.
Answer by vasumathi(46) (Show Source): You can put this solution on YOUR website!
If the twice the reciprocal of the larger of two consecutive integers is subtracted from the reciprocal of the smaller, the result is -5 times the reciprocal of the product of the two integers. Find the integers.
Solution:let x and x+1 be two consecutive integers
then the reciprocal of the larger is 1/(x+1)
and the reciprocal of the smaller is 1/x
twice the reciprocal of the larger = 2/(x+1)
reciprocal of the product of the two integers is
1/x(x+1)
so ...
1/x - 2/(x+1) = -5(1/x(x+1))
(x+1-2x)/(x*(x+1))= -5/(x(x+1))
(1-x)/x*(x+1) = -5/(x*(x+1))
1-x = -5 (multiplied both sides by x(x+1)
now 1-x+x+5 = -5+x+5(added x and 5 on both sides)
6 = x
so x = 6
this is the smaller of the two integers
and its consecutive is x+1 = 6+1 = 7
so the two consecutive integers are 6 and 7
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