1.2. [4] On the sheet, the numbers 1 and $x$, which is not a natural number, are written. In one move, the reciprocal of any of the already written numbers or the sum or difference of two of the written numbers can be written on the sheet. Is it possible for the number $x^{2}$ to appear on the sheet after several moves?

Answer. It is possible.
Solution. For example, the numbers are recorded sequentially:

$$
1, x, \frac{1}{x}, x+1, \frac{1}{x+1}, \frac{1}{x}-\frac{1}{x+1}=\frac{1}{x^{2}+x}, x^{2}+x,\left(x^{2}+x\right)-x=x^{2}
$$