Question

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

Answer 1

Let the no be x

A/Q

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

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