Answer: The positive integer is 4.
Explanation: If we have the integer x, we need to solve:
x - 1/x = 15/4
we multiply all the equation by x.
x^2 - 1 = (15/4)*x
x^2 - (15/4)*x - 1 = 0
now we can solve this quadratic equation and find the value of x
the solutions are:
[tex]x = \frac{15/4 +/-\sqrt{(15/4)^{2} - 4*-1*1 } }{2} = \frac{15/4 +/- \sqrt{(15/4)^{2} + 4 } }{2} = \frac{3.75 +/- 4.25}{2}[/tex]
So the solutions are:
x = (3.75 - 4.25)/2 = -0.25
this is not integer nor positive, so this is not the solution we are looking for.
and the other solution is:
x = (3.75 + 4.25)/2 = 4
this is integer and positive, so this is the solution we are looking for.
