Question

the sum of the natural number and it's resciprocal is 10/3 find the number​

Answer 1

Answer:

method 1.

let the number be x

then it's reciprocal = 1/x

according to question,

x + 1/x = 10/3

or,

$x + \frac{1}{x} = 3 + \frac{1}{3}$

on comparing both sides we get

x = 3 , or x = ⅓

method 2.

on solving the equation

$\frac{ {x}^{2} + 1 }{x} = \frac{10}{3} \\ = > 3 {x}^{2} + 3 = 10x$

=> 3x² - 10x + 3 = 0

=> 3x² -9x - x + 3 = 0

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

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

=> x -3 = 0 , or 3x -1 = 0

=> x = 3 , or ,.x = ⅓.

you are advised to do my method 2. in school exams. when step marking us involved.

I hope it will help you.