Уравнение

[Гост]

[tex]x^{5 } - 2x^{4 } - 2 x^{3 } + 1 = 0[/tex]

[peyo]

[tex]x^{5 } - 2x^{4 } - 2 x^{3 } + 1 = 0[/tex]

Аз мога да потвърдя, че да, това е уравнение.

[Гост]

nechetno, simetrichno...znachi se deli na x+1...natatak davai....

[KOPMOPAH]

Освен очевАдния корен $x=-1$ има още два реални корена, които не са за хора с нежни души.

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$$x^{5}-2\,x^{4}-2\,x^{3}+1=0\;\to\;\begin{gathered}x_{1}=-1\\x_{2}=\dfrac{\sqrt{23\cdot 2^{\frac{5}{3}}\,3^{\frac{7}{4}}\,\sqrt[{6}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{5}}+\sqrt{4\cdot \sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}+19\cdot \sqrt[{3}]{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}+2^{\frac{14}{3}}\,\sqrt[{3}]{3}}\,\left(19\cdot 2\,\sqrt{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}-2^{\frac{29}{6}}\,\sqrt[{3}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}-9\cdot 4\,\sqrt[{6}]{2}\,\sqrt{1099}-173\cdot 4\,\sqrt[{6}]{2}\,\sqrt{3}\right)}}{4\,\sqrt[{4}]{2}\,\sqrt[{12}]{2187}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}\,\sqrt[{4}]{4\cdot \sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}+19\cdot \sqrt[{3}]{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}+2^{\frac{14}{3}}\,\sqrt[{3}]{3}}}+\dfrac{\sqrt{4\cdot \sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}+19\cdot \sqrt[{3}]{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}+2^{\frac{14}{3}}\,\sqrt[{3}]{3}}}{4\,\sqrt[{6}]{2}\,\sqrt[{12}]{2187}\,\sqrt[{6}]{9\,\sqrt{1099}+173\,\sqrt{3}}}+\dfrac{3}{4}\\x_{3}=-\dfrac{\sqrt{23\cdot 2^{\frac{5}{3}}\,3^{\frac{7}{4}}\,\sqrt[{6}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{5}}+\sqrt{4\cdot \sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}+19\cdot \sqrt[{3}]{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}+2^{\frac{14}{3}}\,\sqrt[{3}]{3}}\,\left(19\cdot 2\,\sqrt{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}-2^{\frac{29}{6}}\,\sqrt[{3}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}-9\cdot 4\,\sqrt[{6}]{2}\,\sqrt{1099}-173\cdot 4\,\sqrt[{6}]{2}\,\sqrt{3}\right)}}{4\,\sqrt[{4}]{2}\,\sqrt[{12}]{2187}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}\,\sqrt[{4}]{4\cdot \sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}+19\cdot \sqrt[{3}]{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}+2^{\frac{14}{3}}\,\sqrt[{3}]{3}}}+\dfrac{\sqrt{4\cdot \sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}+19\cdot \sqrt[{3}]{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}+2^{\frac{14}{3}}\,\sqrt[{3}]{3}}}{4\,\sqrt[{6}]{2}\,\sqrt[{12}]{2187}\,\sqrt[{6}]{9\,\sqrt{1099}+173\,\sqrt{3}}}+\dfrac{3}{4}\end{gathered}$$

[peyo]

Освен очевАдния корен $x=-1$ има още два реални корена, които не са за хора с нежни души.

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$$x^{5}-2\,x^{4}-2\,x^{3}+1=0\;\to\;\begin{gathered}x_{1}=-1\\x_{2}=\dfrac{\sqrt{23\cdot 2^{\frac{5}{3}}\,3^{\frac{7}{4}}\,\sqrt[{6}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{5}}+\sqrt{4\cdot \sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}+19\cdot \sqrt[{3}]{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}+2^{\frac{14}{3}}\,\sqrt[{3}]{3}}\,\left(19\cdot 2\,\sqrt{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}-2^{\frac{29}{6}}\,\sqrt[{3}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}-9\cdot 4\,\sqrt[{6}]{2}\,\sqrt{1099}-173\cdot 4\,\sqrt[{6}]{2}\,\sqrt{3}\right)}}{4\,\sqrt[{4}]{2}\,\sqrt[{12}]{2187}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}\,\sqrt[{4}]{4\cdot \sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}+19\cdot \sqrt[{3}]{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}+2^{\frac{14}{3}}\,\sqrt[{3}]{3}}}+\dfrac{\sqrt{4\cdot \sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}+19\cdot \sqrt[{3}]{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}+2^{\frac{14}{3}}\,\sqrt[{3}]{3}}}{4\,\sqrt[{6}]{2}\,\sqrt[{12}]{2187}\,\sqrt[{6}]{9\,\sqrt{1099}+173\,\sqrt{3}}}+\dfrac{3}{4}\\x_{3}=-\dfrac{\sqrt{23\cdot 2^{\frac{5}{3}}\,3^{\frac{7}{4}}\,\sqrt[{6}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{5}}+\sqrt{4\cdot \sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}+19\cdot \sqrt[{3}]{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}+2^{\frac{14}{3}}\,\sqrt[{3}]{3}}\,\left(19\cdot 2\,\sqrt{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}-2^{\frac{29}{6}}\,\sqrt[{3}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}-9\cdot 4\,\sqrt[{6}]{2}\,\sqrt{1099}-173\cdot 4\,\sqrt[{6}]{2}\,\sqrt{3}\right)}}{4\,\sqrt[{4}]{2}\,\sqrt[{12}]{2187}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}\,\sqrt[{4}]{4\cdot \sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}+19\cdot \sqrt[{3}]{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}+2^{\frac{14}{3}}\,\sqrt[{3}]{3}}}+\dfrac{\sqrt{4\cdot \sqrt[{3}]{\left(9\,\sqrt{1099}+173\,\sqrt{3}\right)^{2}}+19\cdot \sqrt[{3}]{2}\,\sqrt[{6}]{3}\,\sqrt[{3}]{9\,\sqrt{1099}+173\,\sqrt{3}}+2^{\frac{14}{3}}\,\sqrt[{3}]{3}}}{4\,\sqrt[{6}]{2}\,\sqrt[{12}]{2187}\,\sqrt[{6}]{9\,\sqrt{1099}+173\,\sqrt{3}}}+\dfrac{3}{4}\end{gathered}$$

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In [17]: for a in solve(x**5 -2*x**4 -2*x**3 +1):
...: print("$",latex(a),"$")
...:
$ -1 $
$ \frac{3}{4} + \frac{\sqrt{\frac{2}{9 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}} + \frac{19}{12} + 2 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}} + \frac{23}{4 \sqrt{\frac{2}{9 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}} + \frac{19}{12} + 2 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}}} + \frac{19}{6}}}{2} $
$ - \frac{\sqrt{\frac{2}{9 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}} + \frac{19}{12} + 2 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}}}{2} + \frac{3}{4} - \frac{\sqrt{- \frac{23}{4 \sqrt{\frac{2}{9 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}} + \frac{19}{12} + 2 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}}} - 2 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}} + \frac{19}{6}}}{2} $
$ - \frac{\sqrt{\frac{2}{9 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}} + \frac{19}{12} + 2 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}}}{2} + \frac{3}{4} + \frac{\sqrt{- \frac{23}{4 \sqrt{\frac{2}{9 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}} + \frac{19}{12} + 2 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}}} - 2 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}} + \frac{19}{6}}}{2} $
$ - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}} + \frac{23}{4 \sqrt{\frac{2}{9 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}} + \frac{19}{12} + 2 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}}} + \frac{19}{6}}}{2} + \frac{3}{4} + \frac{\sqrt{\frac{2}{9 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}} + \frac{19}{12} + 2 \sqrt[3]{\frac{\sqrt{3297}}{144} + \frac{173}{432}}}}{2} $

Красота!

[Гост]

otde znaiti chi sa verni tija otgovori?

[Гост]

kato se razdeli na x+1, kvo sha ostane?

[Гост]

Ако можеше да пишеш грамотно и на български, то щях да се опитам да ти обясня. В случая не виждам смисъл.

[Гост]

Ако можеше да пишеш грамотно и на български, то щях да се опитам да ти обясня. В случая не виждам смисъл.

ti ne mi objasnjavash urok po balagarski, a po matematika...taka che ne se prevzemai