diff options
author | Karl Berry <karl@freefriends.org> | 2009-05-19 18:54:54 +0000 |
---|---|---|
committer | Karl Berry <karl@freefriends.org> | 2009-05-19 18:54:54 +0000 |
commit | 2d248026682e0a02fa2b004a0ad2f13f57d8535c (patch) | |
tree | 7088bbd745de030191c2d843c4b3f4d9d5c46d91 /Master/texmf-dist/doc/latex/kopka/uebungen/kapitel5/ueb5-9.tex | |
parent | eecee5a57aa7fbeb22e0df8440fb3b06c5117fc7 (diff) |
move german latex docs out of texmf-doc
git-svn-id: svn://tug.org/texlive/trunk@13264 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/kopka/uebungen/kapitel5/ueb5-9.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/kopka/uebungen/kapitel5/ueb5-9.tex | 18 |
1 files changed, 18 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/kopka/uebungen/kapitel5/ueb5-9.tex b/Master/texmf-dist/doc/latex/kopka/uebungen/kapitel5/ueb5-9.tex new file mode 100644 index 00000000000..d96ee8386e3 --- /dev/null +++ b/Master/texmf-dist/doc/latex/kopka/uebungen/kapitel5/ueb5-9.tex @@ -0,0 +1,18 @@ +\documentclass{article} +\usepackage{german} +\begin{document} +Die reduzierte kubische Gleichung $y^3 + 3py +2q = 0$ hat f"ur +$D = q^2 + p^3 > 0$ +eine reelle und zwei komplexe L"osungen. Diese lassen sich mit den Abk"urzungen +\[ u = \sqrt[3]{-q + \sqrt{q^2+p^3}},\qquad v = \sqrt[3]{-q - \sqrt{q^2+p^3}} \] +nach der \emph{Cardanischen} Formel als +\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} +darstellen. +\end{document} + |