Question

The sum of a number and its reciprocal is 13/6. find the number

Answer 1

$x + \frac{1}{x} = \frac{13}{6} \text{, x} \neq 0$
$x^{2} - \frac{13}{6}x + 1 = 0$
$6x^{2} - 13x + 6 = 0$
$6x^{2} -9x - 4x + 6 = 0$
$3x(2x - 3) - 2(2x - 3) = 0$
$(3x - 2)(2x - 3) = 0$

So, the numbers are: 3/2 and 2/3