The sum of a natural number and its reciprocal is 10/3 . Find the number.

6. The sum of a natural number and its reciprocal is 10/3 . Find the number.


Sol. Let natural number be ‘x’

 Its reciprocal is 1/x



From the given condition,

x + 1/x = 10/3

Multiplying by 3x, we get

3x2 + 3 = 10x

 3x2 – 10x + 3 = 0

3x2 – 9x – x + 3 = 0

3x (x – 3) – 1 (x – 3) = 0

(3x – 1) (x – 3) = 0

3x – 1 = 0 or x – 3 = 0

3x = 1 or x = 3

x = 1/3  or   x = 3

Natural number cannot be a 1/3

∴ x = 3


∴ The required natural number is 3.