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 $9$