[tex]x + \frac{1}{x} = \frac{13}{6} \text{, x} \neq 0[/tex]
[tex]x^{2} - \frac{13}{6}x + 1 = 0[/tex]
[tex]6x^{2} - 13x + 6 = 0[/tex]
[tex]6x^{2} -9x - 4x + 6 = 0[/tex]
[tex]3x(2x - 3) - 2(2x - 3) = 0[/tex]
[tex](3x - 2)(2x - 3) = 0[/tex]
So, the numbers are: 3/2 and 2/3
