203. $\frac{1}{x^{2}}+2 \frac{1}{x}=1 \frac{1}{4}$.

## Problems of Begh-Edin.

From the treatise "The Essence of the Art of Calculation".
203. Omar's Solution: $z=\frac{1}{x} ; \quad z^{2}+2 z=\frac{5}{4} ;$

$$
\begin{aligned}
& z^{2}+2 z+1=\frac{9}{4} ;(z+1)^{2}=\frac{9}{4} ; z+1=\frac{3}{2} ; z=\frac{1}{2} \\
& z^{2}=\frac{1}{4}, \text { therefore, } x^{2}=4 \text { and } x=2
\end{aligned}
$$

Bega Ed-Din (16th century), a Persian mathematician, author of the treatise "Kolasa-tal-Hisab" ("The Essence of the Art of Calculation"), which served as a guide for the study of mathematics in schools of Hindustan and Persia until the beginning of the 19th century.