1. Let x be the number and 1/x be its reciprocal.
2. Then, since the sum of a number and its reciprocal is 25/12.
3. Multiply 12x to both sides of the equation to get rid of the denominators.
4. Subtract 25x to put the equation in quadratic form
5. We can use the quadratic formula given as (its given in the file)
where a=12, b=-25, and c=12.