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

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:

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.

answer:

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