Question

A natural number is 8/3 more than its reciprocal. Find the number (8/3 is in mixed fraction)

Answer 1

hope it helps uh.....

Answer 2

The natural number is 3 or, -  $\dfrac{1}{3}$.

Step-by-step explanation:

Let the natural number = x

To find, the number = ?

According to question,

x - $\dfrac{1}{x}$ = $\dfrac{8}{3}$

⇒ $\dfrac{x^2-1}{x}$ = $\dfrac{8}{3}$

By crossmultiplication, we get

3$x^2$ - 3 = 8x

⇒ 3$x^2$ - 8x - 3 = 0

⇒ 3$x^2$ - 9x + x - 3 = 0

⇒ 3x(x - 3) + 1(x - 3) = 0

⇒ (3x + 1)(x - 3) = 0

⇒ x - 3 = 0 or, 3x + 1 = 0

⇒ x - 3 = 0 ⇒ x = 3

or, 3x + 1 = 0 ⇒ x = -  $\dfrac{1}{3}$

∴ x = 3 or, -  $\dfrac{1}{3}$

Thus, the natural number is 3 or, -  $\dfrac{1}{3}$.