Question

solve this question the sum of a number and it's reciprocal is 10/3. find the number​

Answer 1

Answer:

3

1/3

Step-by-step explanation:

Let x = the number

 

Then, x + 1/x = 10/3

 

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

$3x^{2} +3=10x$

$3x^{2} - 10x +3 = 0$

$3x^{2} - (9+1)x +3 = 0$

$3x^{2} - 9x - x +3 = 0$

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

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

so,

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

3x-1 = 0 => x = 1/3