Question

Sum of a rational number and its recoprocal is 13/6 find the number

Answer 1

Answer

$x + \frac{1}{x} = \frac{13}{6} \\ \\ = > {x}^{2} + 1 = \frac{13x}{6} \\ \\ = > 6 {x}^{2} + 6 = 13x \\ = > 6 {x}^{2} - 13x + 6 = 0 \\ = > 6 {x}^{2} - 4x - 9x + 6 = 0\\ = > 2x(3x - 2) - 3(3x - 2) = 0 \\ = > (2x - 3)(3x - 2) = 0 \\ = > x = \frac{3}{2} \: or \: \frac{2}{3}$