Question

The sum of a number and its reciprocal is $5\frac{1}{5}$. Find the number.

Answer 1

Let x denote the required number. Then its reciprocal is $\frac{1}{x}$.

By the given condition, $x+\frac{1}{x}=5\frac{1}{5}\to \frac{x^2+1}{x}=\frac{26}{5}$

So, $5x^2-26x+5=0$$\to 5x^2-25x-x+5=0$

That is, $(5x-1)(x-5)=0\to x=5$ or $\frac{1}{5}$

Thus, the required numbers are $5,\frac{1}{5}$.