Question

The difference of two positive integers is 4 and the difference of their reciprocals is $\frac{1}{24}$. Find the integers.

• A. $0,12$
• B. $3,2$
• C. $8,12$
• D. $1,12$

Answer 1

The correct option is C $8,12$

Difference of two positive number be $4$ hence if one number is $x$ then other will be $4+x$

difference of reciprocal be $\frac{1}{24}$

$\frac{1}{x}-\frac{1}{x+4}=\frac{1}{24}$

$\frac{4}{x^2+4x}=\frac{1}{24}$

$x^2+4x=96$

$x^2+4x-96=0$

$x^2+12x-8x-96=0$

$x(x+12)-8(x+12)=0$

$(x-8)(x+12)=0$

$x=8$ or $x=-12$

since numbers are positive

$x=8;x+4=12$

integers are $8,12$