Question

Which number(s) is(are) equal to its (their) square?

Answer 1

If \(x\) is the number to find, its square is \(x^{2}\).
\(x\) is equal to its square hence: \(x=x^{2}\)
Solve the above equation by factoring. First write with right side equal to zero.
\[
\begin{aligned}
&x-x^{2}=0 \\
&x(1-x)=0
\end{aligned}
\]
solutions: \(x=0\) and \(x=1\)
Check answers.
1) \(x=0\), its square is \(0^{2}=0\). Hence \(x\) and its square are equal.
2) \(x=1\), its square is \(1^{2}=1\). Hence \(x\) and its square are equal.