Question

The sum of a number and its reciprocal is 65/8. Find the numbers.

Answer 1

Answer: 8 and
`(1)/(8)`

Explanation:

x +
`(1)/(x)` =
`(65)/(8)`

need to eliminate the denominator:

x(8x) +
`(1)/(x)`(8x) =
`(65)/(8)`(8x)

8x² + 8 = 65x

8x² - 65x + 8 = 0

(8x -1)(x - 8) = 0

(8x -1) = 0 (x - 8) = 0

x =
`(1)/(8)` x = 8