The difference of the reciprocals of two consecutive integers is 1/72. What are the two integers?

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Answer 1 · 2017-04-26T12:42:46

#8,9#

Let the consecutive integers be #x and x+1#

The difference of their reciprocals is equal to #1/72#

#rarr1/x-1/(x+1)=1/72#

Simplify the left side of the equation

#rarr((x+1)-(x))/((x)(x+1))=1/72#

#rarr(x+1-x)/(x^2+x)=1/72#

#rarr1/(x^2+x)=1/72#

The numerators of the fractions are equal, so as the denominators

#rarrx^2+x=72#

#rarrx^2+x-72=0#

Factor it

#rarr(x+9)(x-8)=0#

Solve for the values of #x#

#color(green)(rArrx=-9,8#

Consider the positive value to get the correct answer

So, the integers are #8# and #9#