the sum of a number and its reciprocal is $$2 \frac{1}{30}$$. Then , the number is:​

Correct option is C

Given:

​$$x + \frac{1}{x} = 2\frac{1}{30} = \frac{61}{30}$$​​

Solution:

​$$x + \frac{1}{x} = \frac{61}{30} \\ \ \\ x^2 + 1 = \frac{61}{30}x \\ \ \\ x^2 - \frac{61}{30}x + 1 = 0$$​​

Using quadratic formula:

​$$x = \frac{\frac{61}{30} \pm \sqrt{\left(\frac{61}{30}\right)^2 - 4(1)(1)}}{2} \\ \ \\ x = \frac{\frac{61}{30} \pm \sqrt{\left(\frac{3721}{900}-\frac{3600}{900}\right)}}{2}$$ 

​​​​$$x = \frac{\frac{61}{30} \pm \sqrt{\frac{121}{900}}}{2} = \frac{\frac{61}{30} \pm \frac{11}{30}}{2}$$​​

So:

​$$x = \frac{61 + 11}{30} \div 2 = \frac{72}{30} \div 2 = \frac{72}{60} = \frac{6}{5}$$​​

​$$x = \frac{61 - 11}{30} \div 2 = \frac{50}{30} \div 2 = \frac{50}{60} = \frac{5}{6}$$​​