Question

The difference of a positive integer and its inverse is 15/4. find the integer

Answer 1

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
`x= (3.75+- √((-3.75)^2-(4*-1*1)) )/(2) = (3.75+- √(14.0625+4) )/(2) = 4, -0.25.`

Since it has to be a positive integer, we get x=4