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Diffstat (limited to 'Master/texmf-doc/doc/english/guide-to-latex/exercises/chap7/exer7-2.tex')
-rw-r--r-- | Master/texmf-doc/doc/english/guide-to-latex/exercises/chap7/exer7-2.tex | 10 |
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diff --git a/Master/texmf-doc/doc/english/guide-to-latex/exercises/chap7/exer7-2.tex b/Master/texmf-doc/doc/english/guide-to-latex/exercises/chap7/exer7-2.tex deleted file mode 100644 index 56b238f25b8..00000000000 --- a/Master/texmf-doc/doc/english/guide-to-latex/exercises/chap7/exer7-2.tex +++ /dev/null @@ -1,10 +0,0 @@ -\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 -\[ y_1 = u + v,\quad y_2 = -\frac{u+v}{2} + \frac{i}{2}\sqrt{3}(u - v),\quad - y_3 = -\frac{u+v}{2} - \frac{i}{2}\sqrt{3}(u-v) \] -where -\[ u = \sqrt[3]{-q + \sqrt{q^2+p^3}},\qquad v = \sqrt[3]{-q - \sqrt{q^2+p^3}} \] -\end{document} - |