The sum of a number and its reciprocal is 10/3, then the numbers are

Let the number be x and 1/x,
Then, x + 1/x = 10/3
⇒ (x² + 1)/x = 10/3
⇒ 3x² - 10x + 3 = 0
⇒ 3x² - 9x - x + 3 = 0
⇒ 3x(x - 3) -1 (x - 3) = 0
⇒ (3x - 1) (x - 3) = 0
∴ x = 1/3, x = 3