Question

Write the rational numbers that are equal to their reciprocals.

Answer 1

Determine the rational numbers that are equal to their reciprocals.

The rational number would seem to have the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q$ is not equal to $0$.

Let $x$ be a rational number that is $x\in Q$.

As per the given question,

$$\begin{gathered} x=\frac{1}{x} \\ \Rightarrow x^2=1 \\ \Rightarrow x=\pm 1 \end{gathered}$$

Hence, the rational numbers equal to their reciprocal are $1$and $-1$.