Question

The sum of a number and its reciprocal is $2\frac{1}{30}$. Find the number.

Answer 1

Let the required number be $x$.

Then,

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

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

$30x^2-61x+30=0$

$30x^2-36x-25x+30=0$

$(6x-5)(5x-6)=0$

$x=\frac{5}{6}$ or $x=\frac{6}{5}$.

Hence, the required number is $\frac{5}{6}$ or $\frac{6}{5}$.