the sum of a number and its reciprocal is 5/12 find the number

First set up an equation that captures the conditions of the problem. Let x = the unknown number. Its reciprocal is 1/x. So you have

x + 1/x = 5/12.

Now manipulate this to get a quadratic equation which you can solve. You can subtract 5/12 from both sides of the equation so the right hand side becomes 0, then multiply throgh by 12x to get a quadratic equation, and then apply the quadratic formula to solve. You will find that the answer is a complex number (involves square roots of negative numbers).