The sum of a number and its reciprocal is 8. find this number

You have said that                 x + 1/x = 8

Multiply each side by 'x' :       x² + 1 = 8x

Subtract 8x from each side:    x² - 8x + 1 = 0

Solving this quadratic equation by means of the quadratic formula,
(the procedure is left as an exercise for the student), the two
solutions are:

x = 4 + √15 = 7.873  (rounded)
and
x = 4 - √15 = 0.127  (rounded)