Question

The sum of a natural number and its reciprocal is $\frac{10}{3}$. Find the number

Answer 1

Let the number be $x$
Then, $x+\frac{1}{x}=\frac{10}{3}$
$3x^2+3=10x$
$3x^2-10x+3=0$
$3x^2-9x-x+3=0$
$(3x-1)(x-3)=0$
$x=3,\frac{1}{3}$
Since, $x$ is a natural number, $x=3$