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authorDavid A. Madore <david@procyon>2012-03-15 17:51:46 +0100
committerDavid A. Madore <david@procyon>2012-03-15 17:53:27 +0100
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[radicaux] Remaniement de la formule de cos(2π/13).
Diffstat (limited to 'chapitres/radicaux.tex')
-rw-r--r--chapitres/radicaux.tex12
1 files changed, 9 insertions, 3 deletions
diff --git a/chapitres/radicaux.tex b/chapitres/radicaux.tex
index 09abca7..23cd309 100644
--- a/chapitres/radicaux.tex
+++ b/chapitres/radicaux.tex
@@ -709,9 +709,15 @@ vaut $\sqrt{-11}$. On obtient finalement :
\[
\begin{array}{rl}
\displaystyle\cos\frac{2\pi}{13}
-&\displaystyle= - \frac{1}{12} + \frac{1}{12} \, \sqrt{13} + \frac{1}{24} {\left(-1 + \sqrt{-3}\right)} \, \root3\of{-\frac{65}{2} - \frac{39}{2} \, \sqrt{-3}}
-- \frac{1}{24} \, {\left(1 + \sqrt{-3}\right)} \root3\of{-\frac{65}{2} + \frac{39}{2} \, \sqrt{-3}}\\
-&\displaystyle + \frac{1}{24} {\left(1 + \sqrt{-3}\right)} \, \root6\of{-\frac{4381}{2} - \frac{195}{2} \, \sqrt{-3}} - \frac{1}{24} \, {\left(-1 + \sqrt{-3}\right)} \root6\of{-\frac{4381}{2} + \frac{195}{2} \, \sqrt{-3}}\\
+&\displaystyle= - \frac{1}{12} + \frac{1}{12} \, \sqrt{13}\\
+&\displaystyle + \frac{1}{24} \root3\of{\frac{13}{2}}
+\Big(
+ (-1 + \sqrt{-3}) \, \root3\of{-5 - 3 \, \sqrt{-3}}
++ (-1 - \sqrt{-3}) \, \root3\of{-5 + 3 \, \sqrt{-3}} \Big)\\
+&\displaystyle + \frac{1}{24} \root6\of{\frac{13}{2}}
+\Big(
+ (1 + \sqrt{-3}) \, \root6\of{-337 - 15 \, \sqrt{-3}}
++ (1 - \sqrt{-3}) \, \root6\of{-337 + 15 \, \sqrt{-3}} \Big)\\
\end{array}
\]