From a683c3d7e9fac38ec713f23fb6b9d2c7143aea82 Mon Sep 17 00:00:00 2001
From: Karl Berry <karl@freefriends.org>
Date: Sat, 23 May 2009 00:23:51 +0000
Subject: move english latex doc out of texmf-doc

git-svn-id: svn://tug.org/texlive/trunk@13412 c570f23f-e606-0410-a88d-b1316a301751
---
 .../doc/latex/guide-to-latex/exercises/chap7/exer7-9.tex     | 12 ++++++++++++
 1 file changed, 12 insertions(+)
 create mode 100644 Master/texmf-dist/doc/latex/guide-to-latex/exercises/chap7/exer7-9.tex

(limited to 'Master/texmf-dist/doc/latex/guide-to-latex/exercises/chap7/exer7-9.tex')

diff --git a/Master/texmf-dist/doc/latex/guide-to-latex/exercises/chap7/exer7-9.tex b/Master/texmf-dist/doc/latex/guide-to-latex/exercises/chap7/exer7-9.tex
new file mode 100644
index 00000000000..3a104cd3ba0
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/guide-to-latex/exercises/chap7/exer7-9.tex
@@ -0,0 +1,12 @@
+\documentclass{article}
+\begin{document}
+The reduced cubic equation $y^3 + 3py +2q = 0$ has one real and two complex
+solutions when $D = q^2 + p^3 > 0$. These are given by Cardan's formula as
+\begin{equation} y_1 = u + v \end{equation}
+\begin{equation} y_2 = -\frac{u+v}{2} + \frac{i}{2}\sqrt{3}(u-v) \end{equation}
+\begin{equation} y_3 = -\frac{u+v}{2} - \frac{i}{2}\sqrt{3}(u-v) \end{equation}
+where
+\[ u = \sqrt[3]{-q + \sqrt{q^2+p^3}},\qquad v = \sqrt[3]{-q - \sqrt{q^2+p^3}} \]
+\end{document}
+
+
-- 
cgit v1.2.3

