[A2/H3/E4] Solved

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diff --git a/Year 2/Algebra/Homework3/Exercise4.pdf b/Year 2/Algebra/Homework3/Exercise4.pdf
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diff --git a/Year 2/Algebra/Homework3/Exercise4.tex b/Year 2/Algebra/Homework3/Exercise4.tex
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+% Document MUST be built with XeLaTeX!
+\documentclass[11pt,a4paper]{article}
+
+\usepackage[margin=1.5cm]{geometry}
+
+% Поддръжка на български език
+% Thanks to https://tex.stackexchange.com/a/136926
+\usepackage{fontspec}
+\defaultfontfeatures{Ligatures=TeX}
+\setmainfont{CMU Serif}
+\setsansfont{CMU Sans Serif}
+
+\usepackage[bulgarian,english]{babel}
+
+\usepackage{amsmath}            % Математически символи
+\usepackage{amssymb}
+\usepackage{mathtools}
+\usepackage{amsfonts}           % Още математически символи
+\usepackage{cancel}             % Зачертаване
+\usepackage[dvipsnames]{xcolor} % Цветни кутийки + допълнителни цветове
+\usepackage{indentfirst}        % Индентация на параграф след секция
+
+\usepackage{enumitem}
+\setlist[enumerate]{label=\arabic*.}
+
+\renewcommand{\thesection}{}
+
+\let\oldforall\forall
+\renewcommand{\forall}{\; \oldforall}
+
+\let\oldexist\exists
+\renewcommand{\exists}{\; \oldexist}
+
+\usepackage[pdfauthor={Камен Димитров Младенов, КН Летен семестър, 2023},
+		    pdftitle={Домашна работа 3 по А2, Зад 4},
+		    pdfsubject={},
+		    pdfkeywords={},
+		    colorlinks=true,
+		    urlcolor=blue]{hyperref}
+
+\title{\vspace{-1.5cm}Домашно №3, Задача 4 по Алгебра 2 на Компютърни Науки}
+\author{Камен Димитров Младенов, Група 6}
+\date{31 Май 2023}
+
+\begin{document}
+
+\maketitle
+
+\section{Решение}
+
+\begin{align*}
+	& \left| \begin{array}{ll}
+		x_1 + x_2 + x_3 + x_4 + x_5 & = 3 \\
+		x_1 x_2 + x_1 x_3 + x_1 x_4 + x_1 x_5 + x_2 x_3 + x_2 x_4 + x_2 x_5 + x_3 x_4 + x_3 x_5 + x_4 x_5 & = -5 \\
+		x_1 x_2 x_3 + x_1 x_2 x_4 + x_1 x_2 x_5 + x_1 x_3 x_4 + x_1 x_3 x_5 + x_1 x_4 x_5 + x_2 x_3 x_4 + x_2 x_3 x_5 + x_2 x_4 x_5 + x_3 x_4 x_5 & = -p \\
+		x_1 x_2 x_3 x_4 + x_1 x_2 x_3 x_5 + x_1 x_2 x_4 x_5 + x_1 x_3 x_4 x_5 + x_2 x_3 x_4 x_5 & = q \\
+		x_1 x_2 x_3 x_4 x_5 & = -r \\
+		x_1 + x_2 + x_3 = 2(x_4 + x_5) \\
+		x_4 x_5 = 6(x_1 x_2 + x_1 x_3 + x_2 x_3) = 3 x_1 x_2 x_3
+	\end{array} \right. \\
+	& \text{От равенства 1 и 6} \implies 2(x_4 + x_5) + x_4 + x_5 = 3 \iff x_4 + x_5 = 1 \\
+	& \left| \begin{array}{ll}
+		x_4 + x_5 & = 1 \\
+		(x_4 + x_5)(x_1 + x_2 + x_3) + x_1 x_2 + x_1 x_3 + x_2 x_3 + x_4 x_5 & = -5 \\
+		(x_4 + x_5)(x_1 x_2 + x_1 x_3 + x_2 x_3) + x_1 x_2 x_3 + x_1 x_4 x_5 + x_2 x_4 x_5 + x_3 x_4 x_5 & = -p \\
+		(x_4 + x_5) x_1 x_2 x_3 + x_1 x_2 x_4 x_5 + x_1 x_3 x_4 x_5 + x_2 x_3 x_4 x_5 & = q \\
+		x_1 x_2 x_3 x_4 x_5 & = -r \\
+		x_1 + x_2 + x_3 = 2 \\
+		x_4 x_5 = 6(x_1 x_2 + x_1 x_3 + x_2 x_3) = 3 x_1 x_2 x_3
+	\end{array} \right. \\
+	& \text{От равенства 2 и 6} \implies x_1 x_2 + x_1 x_3 + x_2 x_3 + x_4 x_5 = -7 \quad \text{ от равенство 7 } \implies \frac{1}{6} x_4 x_5 + x_4 x_5 = -7 \\
+	& \iff \frac{7}{6}x_4 x_5 = -7 \iff x_4 x_5 = -6 \\
+	& \left| \begin{array}{ll}
+		x_4 + x_5 & = 1 \\
+		x_4 x_5 & = -6 \\
+		(x_4 x_5)(x_1 + x_2 + x_3) + x_1 x_2 + x_1 x_3 + x_2 x_3 + x_1 x_2 x_3 & = -p \\
+		(x_4 x_5)(x_1 x_2 + x_1 x_3 + x_2 x_3) + x_1 x_2 x_3 & = q \\
+		(x_4 x_5) x_1 x_2 x_3 & = -r \\
+		x_1 + x_2 + x_3 = 2 \\
+		-6 = 6(x_1 x_2 + x_1 x_3 + x_2 x_3) = 3 x_1 x_2 x_3
+	\end{array} \right. \\
+	& \text{От равенства 3 и 2 и 6} \implies -6 . 2 + (x_1 x_2 + x_1 x_3 + x_2 x_3) + x_1 x_2 x_3 = -p \quad \text{ от рав. 7 } \\
+	& \implies -12 - 1 + x_1 x_2 x_3 = -p \iff x_1 x_2 x_3 = 13 - p \quad \text{ от рав 7 } \implies -2 = 13 - p \implies p = 15 \\
+	& \text{От равенства 4 и 2 и 7} \implies -6 . (-1) + x_1 x_2 x_3 = q \quad \text{ от рав 7 } \implies 6 + (-2) = q \implies q = 4 \\
+	& \text{От равенства 5 и 2 и 7} \implies (-6) . (-2) = -r \implies r = -12
+\end{align*}
+
+\end{document}
\ No newline at end of file