Task B-2.3. One solution of the equation $x^{2}-2 x+k=0$ is the square of the other solution. Determine all values of the number $k$ for which this is true.
## First solution.

$$
\begin{aligned}
& x_{1,2}=\frac{2 \pm \sqrt{4-4 k}}{2}=1 \pm \sqrt{1-k} \\
& x_{1}=x_{2}^{2} \\
& 1+\sqrt{1-k}=(1-\sqrt{1-k})^{2} \\
& 1+\sqrt{1-k}=1-2 \sqrt{1-k}+1-k \\
& 3 \sqrt{1-k}=1-k \\
& 9-9 k=k^{2}-2 k+1
\end{aligned}
$$