Final answer:
To find the possible values of the number, we can set up an algebraic equation and solve for x. The possible values of the number are 0.625 and 8.0.
Step-by-step explanation:
To solve this problem, we can use algebraic equations. Let's assume the number is x. The reciprocal of the number is 1/x. The sum of the number and its reciprocal is given as 26/5. So, we can write the equation as x + 1/x = 26/5.
To solve this equation, we can multiply both sides by the common denominator, which is 5x. This gives us 5x^2 + 5 = 26x.
Next, we can rearrange the equation by moving all the terms to one side: 5x^2 - 26x + 5 = 0.
Finally, we can factorize or use the quadratic formula to solve for x. In this case, the possible values of x are approximately 0.625 and 8.0.