Question

the sum of a number and its reciprocal is 2 1/6.find the number?​

Answer 1

Answer:

let the number is

$let \: the \: number \: is \: x \: \\ then \: according \: to \: quation \\ x + \frac{1}{x} = 2 \frac{1}{6} \\ \frac{ {x }^{2} + 1}{x} = \frac{13}{6} \\ cross \: multipication \\ 6 {x}^{2} + 6 = 13x \\ 6 {x }^{2} - 13x + 6 = 0 \\ 6 {x}^{2} - 9x - 4x + 6 = 0 \\ 3x(2x - 3) - 2(2x - 3) = 0\\ (2x - 3)(3x - 2) = 0 \\ 2x - 3 = 0 \\ x = \frac{3}{2} \\ 3x - 2 = 0 \\ x = \frac{2}{3}$