Hi Patricia,
You need to translate the English into math. . . if a number is represented by X, then its reciprocal is 1/X. The sum is 17/4.
So X + 1/X = 17/4
When you add fractions, you need a common denominator. Let's make X the common denominator. So we have to multiply the top and bottom of the first fraction by X.
X^2/X + 1/X = 17/4
(X^2 + 1)/X = 17/4
Now cross multiply--> 4X^2 + 4 = 17X
Subtract 17X from both sides-->4X^2 - 17X + 4 = 0
Plug into the quadratic equation where a = 4 b = -17 c = 4
X = (17 +/- sq root (289 - 64))/8
X = (17 + 15)/8 X = (17 - 15)/8
X = 4 X = 1/4
Adding 1/4 and its reciprocal -->1/4 + 4 = 4 1/4 which is the same thing as 17/4.
Adding 4 and its reciprocal--> 4 + 1/4 = 4 1/4
Dan
