Question

the sum of a natural number and its reciprocal is 65/8. Find the number. plz ans ASAP

Answer 1

Hey


Let the number be x .
It's reciprocal be 1/x .

A/q ,
$x + \frac{1}{x} = \frac{65}{8}$

$= > \frac{ {x}^{2} + 1 } {x} = \frac{65}{8}$

$= > 8 {x}^{2} + 8 = 65x$
$= > 8 {x}^{2} - 65x + 8 = 0$


$= > 8 {x}^{2} -64x - x + 8 = 0$

$= > 8x(x - 8) - 1(x - 8) = 0$

$= > (8x - 1)(x - 8) = 0$


So , x = 8 or x = 1/8

Thanks :)