Question

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

Answer 1

Let the required no. be x.

Then its reciprocal be = 1/x.

According to the question,

x + (1/x )= 10/3

(x^2 + 1)/x = 10/3

3x^2 + 3 = 10x

3x^2- 10x + 3 = 0

3x^2- 9x - x + 3 = 0

3x (x-3) - 1 (x-3) = 0

3x - 1 = 0 or x - 3 = 0

x = 1/3 or x = 3.

... the reqiured number is 3