Question

3. The sum of a fraction and 3 times its reciprocal is 31/6. What is the fraction ?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Required fractions are 9/2 and 2/3.

Step-by-step explanation:

let x be the fraction.

According tot he question,

x + 3 × (1/x) = 31/6

x + 3/x = 31/6

(x² + 3)/x = 31/6

6x² - 31x + 18  = 0

Using Quadratic Formula,

$x=\frac{-(-31)\pm\sqrt{(-31)^2-4\times6\times18}}{2\times6}$

$x=\frac{31\pm\sqrt{961-432}}{12}$

$x=\frac{31\pm\sqrt{961-432}}{12}$

$x=\frac{31\pm23}{12}$

$x=\frac{31+23}{12}\:\:and\:\:x=\frac{31-23}{12}$

$x=\frac{54}{12}\:\:and\:\:x=\frac{8}{12}$

$x=\frac{9}{2}\:\:and\:\:x=\frac{2}{3}$

Therefore, Required fractions are 9/2 and 2/3.