Question

Q....
If the sum of a rational no & it's reciprocal is 10/3. Find the no.

Answer 1

                    ___________________________

Let the no. is x.

A/Q,

⇒ x + ( 1/x ) =10/3

⇒ ( x² + 1 ) / x = 10/3

⇒ 3 ( x² + 1 ) = 10 x

⇒ 3 x² + 3 = 10 x

⇒ 3x² - 10 x + 3 = 0

⇒ 3 x² - 9 x - x + 3 = 0

⇒ 3 x ( x - 3 ) - 1 ( x - 3 ) = 0

⇒ ( x - 3 ) ( 3 x - 1 ) = 0


∴  x = 3 or 1/3.




Hope it helps !