Question

The sum of a number and its reciprocal is 10 by 3. find the number.​

Answer 1

Let x = the number

 

Then, x + 1/x = 10/3

 

Multiply through by the LCD, 3x, to get 3x2 + 3 = 10x

 

3x2 - 10x + 3 = 0

 

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

 

So, x = 1/3 or x = 3

 

Answer 2

Step-by-step explanation:

let the number be x

it is given that the sum of the number (x) and its reciprocal (1/x)

x+ 1/x = 10/3

x^2+1/x =10/3

cross multiply both,

10x = 3x^2+3

3x^2-10x+3 = 0

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

3x (x-3)-1 (x-3)

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

x = 1/3,3