If the integer is x, and the inverse is 1/x, we have x-1/x=15/4 (since difference is subtraction). Multiplying both sides by x, we get x²-1=15x/4. Next, we can subtract 15x/4=3.75x from both sides to get x²-3.75x-1=0. Using the quadratic formula, we get [tex]x= \frac{3.75+- \sqrt{(-3.75)^2-(4*-1*1)} }{2}
= \frac{3.75+- \sqrt{14.0625+4} }{2}
= 4, -0.25. [/tex]
Since it has to be a positive integer, we get x=4
