Question

The sum of a rational number and it's reciprocal is 13/6. find the number?​

Answer 1

x=2/3 or x=3/2

Explanation:

x + (1/x) = 13/6

(x2 + 1)/x = 13/6

6x2 – 13x + 6 = 0

6x2 – 9x – 4x + 6 = 0

(3x – 2) (2x – 3) = 0

x = 2/3 or x = 3/2

Answer 2

Explanation:

Let,

Number = x

x + 1/x = 13/6

x² + 1/x = 13/6

6(x² + 1) = 13(x)

6x² + 6 = 13 x

6x² - 13x + 6 = 0

6x² - (9x + 4x) + 6 = 0

6x² - 9x - 4x + 6 = 0

(3x - 2)(2x - 3) = 0

x = 3/2 & 2/3

Hence,

The number would be ⅔ or ³/2