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Which number(s) is(are) equal to its (their) square?
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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 $x=1$
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.
by Platinum (130,878 points)

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