The sum of a number and its reciprocal is 13/6. Find the number.

The reciprocal of a number is the number that multiplied
to original number, gives 1.

We'll take the x number and
it's reciprocal, 1/x.

We'll verify the
constraint:

x*(1/x)=1

Now,
we'll impose the constraint from enunciation:

x + 1/x =
13/6

We'll mutliply by 6x all
over:

6x^2 + 6 = 13x

We'll
move all terms to one side:

6x^2 - 13x + 6 =
0

We'll apply quadratic
formula:

x1= [13+sqrt(169 -
144)]/12

x1 = (13+5)/12

x1 =
18/12

x1 = 3/2

x2 =
(13-5)/12

x2 = 8/12

x2 =
2/3

The number could be:x= 3/2 or x =
2/3.