Question 1134880
let the number be x.


it's reciprocal would then be 1/x


you are given that the sum of the number and its reciprocal is equal to 17/4.


that means that x + 1/x = 17/4


place the expression on the left side of this equation under a common denominator and the equation becomes:


(x^2 + 1) / x = 17 / 4


cross multiply to get (x^2 + 1) * 4 = x * 17


simplify to get 4 * x^2 + 4 = 17 * x


subtract 17 * x from both sides of the equation to get 4 * x^2 - 17 * x + 4 = 0


factor this equation to get  (4x-1) * (x-4) = 0


solve for x to get x = 1/4 or x = 4.


if you let x = 4, then its reciprocal is 1/4 and 4 + 1/4 is equal to 17/4.


if you let x = 1/4, then its reciprocal is 4 and 1/4 + 4 = 17/4.


the number can either be 4 or 1/4.


either one will get you the correct answer.