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%%% file:      s2.tex                                                        %%%
%%% author:    Ján Komara                                                    %%%
%%% email:     komara@fmph.uniba.sk                                          %%%
%%% copyright: public domain                                                 %%%
%%% version:   2021/10/15                                                    %%%
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\begin{document}

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\title{2. domáca úloha z predmetu 1-AIN-121 Matematika (1) ZS 2021/22}

\author{Ján Komara}

%\date{}
\date{\today}

\maketitle

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\section*{1. príklad}

Koľko celočíselných riešení má systém dvoch nerovníc
\begin{align}
x_1 + x_2 & < 4
\label{lt1}
\\
x_1 + x_2 + x_3 + x_4 + x_5 + x_6 & < 17
,
\label{lt2}
\end{align}
ak vyžadujeme, aby platilo
\[
-1 \leq x_1
\quad
2 \leq x_2
\quad
-3 \leq x_3
\quad
4 \leq x_4
\quad
-5 \leq x_5
\quad
6 \leq x_6
.
\]

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\subsection*{Riešenie 1. príkladu}

Táto časť obsahuje riešenie 1. príkladu.

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\section*{2. príklad}

Určite koeficient pri $x^6$ vo výraze $\left(5 - 4x^3 + \frac{3}{x^2}\right)^7$.

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\subsection*{Riešenie 2. príkladu}

Táto časť obsahuje riešenie 2. príkladu.

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\section*{3. príklad}

Dvaja učitelia skúšajú súčasne skupinu 8 študentov, každý jeden predmet.
Každý študent odpovedá z jedného predmetu 30 minút.
Koľko existuje rozvrhov skúšania, ak požadujeme,
aby skúšky skončili za štyri hodiny?

\emph{Pokyny.}
Výsledok vyjadrite pomocou súčtovej notácie $\Sigma$.

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\subsection*{Riešenie 3. príkladu}

Táto časť obsahuje riešenie 3. príkladu.

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\end{document}

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