Sr Examen
Factorizar el polinomio x^6+x^2+1
Solución
Factorización
[src]
/ / / ____________ \\ / / ____________ \\\ / / / ____________ \\ / / ____________ \\\ / / / ____________ \\ / / ____________ \\\ / / / ____________ \\ / / ____________ \\\
| | | 3 ___ 6 ___ 2/3 5/6 3 / ____ || | | 3 ___ 6 ___ 2/3 5/6 3 / ____ ||| | | | 3 ___ 6 ___ 2/3 5/6 3 / ____ || | | 3 ___ 6 ___ 2/3 5/6 3 / ____ ||| | | | 3 ___ 6 ___ 2/3 5/6 3 / ____ || | | 3 ___ 6 ___ 2/3 5/6 3 / ____ ||| | | | 3 ___ 6 ___ 2/3 5/6 3 / ____ || | | 3 ___ 6 ___ 2/3 5/6 3 / ____ |||
| | | \/ 2 *\/ 3 2 *3 *\/ 9 + \/ 93 || | | \/ 2 *\/ 3 2 *3 *\/ 9 + \/ 93 ||| | | | \/ 2 *\/ 3 2 *3 *\/ 9 + \/ 93 || | | \/ 2 *\/ 3 2 *3 *\/ 9 + \/ 93 ||| | | | \/ 2 *\/ 3 2 *3 *\/ 9 + \/ 93 || | | \/ 2 *\/ 3 2 *3 *\/ 9 + \/ 93 ||| | | | \/ 2 *\/ 3 2 *3 *\/ 9 + \/ 93 || | | \/ 2 *\/ 3 2 *3 *\/ 9 + \/ 93 |||
| |atan|------------------------------------------------------------------ + ------------------------------------------------------------------------------|| |atan|------------------------------------------------------------------ + ------------------------------------------------------------------------------||| | |atan|------------------------------------------------------------------ + ------------------------------------------------------------------------------|| |atan|------------------------------------------------------------------ + ------------------------------------------------------------------------------||| | |atan|------------------------------------------------------------------ + ------------------------------------------------------------------------------|| |atan|------------------------------------------------------------------ + ------------------------------------------------------------------------------||| | |atan|------------------------------------------------------------------ + ------------------------------------------------------------------------------|| |atan|------------------------------------------------------------------ + ------------------------------------------------------------------------------|||
| | | 2/3 2/3 / ____________ ____________\|| | | 2/3 2/3 / ____________ ____________\||| | | | 2/3 2/3 / ____________ ____________\|| | | 2/3 2/3 / ____________ ____________\||| | | | 2/3 2/3 / ____________ ____________\|| | | 2/3 2/3 / ____________ ____________\||| | | | 2/3 2/3 / ____________ ____________\|| | | 2/3 2/3 / ____________ ____________\|||
| | | 3 ___ 2/3 3 ____ / ____\ 2/3 3 ___ / ____\ | 3 ____ 3 / ____ 3 ___ 2/3 2/3 3 ___ 3 / ____ ||| | | 3 ___ 2/3 3 ____ / ____\ 2/3 3 ___ / ____\ | 3 ____ 3 / ____ 3 ___ 2/3 2/3 3 ___ 3 / ____ |||| | | | 3 ___ 2/3 3 ____ / ____\ 2/3 3 ___ / ____\ | 3 ____ 3 / ____ 3 ___ 2/3 2/3 3 ___ 3 / ____ ||| | | 3 ___ 2/3 3 ____ / ____\ 2/3 3 ___ / ____\ | 3 ____ 3 / ____ 3 ___ 2/3 2/3 3 ___ 3 / ____ |||| | | | 3 ___ 2/3 3 ____ / ____\ 2/3 3 ___ / ____\ | 3 ____ 3 / ____ 3 ___ 2/3 2/3 3 ___ 3 / ____ ||| | | 3 ___ 2/3 3 ____ / ____\ 2/3 3 ___ / ____\ | 3 ____ 3 / ____ 3 ___ 2/3 2/3 3 ___ 3 / ____ |||| | | | 3 ___ 2/3 3 ____ / ____\ 2/3 3 ___ / ____\ | 3 ____ 3 / ____ 3 ___ 2/3 2/3 3 ___ 3 / ____ ||| | | 3 ___ 2/3 3 ____ / ____\ 2/3 3 ___ / ____\ | 3 ____ 3 / ____ 3 ___ 2/3 2/3 3 ___ 3 / ____ ||||
| | | \/ 2 *3 \/ 12 *\9 + \/ 93 / 2 *\/ 3 *\9 + \/ 93 / | \/ 12 *\/ 9 + \/ 93 \/ 2 *3 2 *\/ 3 *\/ 9 + \/ 93 ||| | | \/ 2 *3 \/ 12 *\9 + \/ 93 / 2 *\/ 3 *\9 + \/ 93 / | \/ 12 *\/ 9 + \/ 93 \/ 2 *3 2 *\/ 3 *\/ 9 + \/ 93 |||| | | | \/ 2 *3 \/ 12 *\9 + \/ 93 / 2 *\/ 3 *\9 + \/ 93 / | \/ 12 *\/ 9 + \/ 93 \/ 2 *3 2 *\/ 3 *\/ 9 + \/ 93 ||| | | \/ 2 *3 \/ 12 *\9 + \/ 93 / 2 *\/ 3 *\9 + \/ 93 / | \/ 12 *\/ 9 + \/ 93 \/ 2 *3 2 *\/ 3 *\/ 9 + \/ 93 |||| | | | \/ 2 *3 \/ 12 *\9 + \/ 93 / 2 *\/ 3 *\9 + \/ 93 / | \/ 12 *\/ 9 + \/ 93 \/ 2 *3 2 *\/ 3 *\/ 9 + \/ 93 ||| | | \/ 2 *3 \/ 12 *\9 + \/ 93 / 2 *\/ 3 *\9 + \/ 93 / | \/ 12 *\/ 9 + \/ 93 \/ 2 *3 2 *\/ 3 *\/ 9 + \/ 93 |||| | | | \/ 2 *3 \/ 12 *\9 + \/ 93 / 2 *\/ 3 *\9 + \/ 93 / | \/ 12 *\/ 9 + \/ 93 \/ 2 *3 2 *\/ 3 *\/ 9 + \/ 93 ||| | | \/ 2 *3 \/ 12 *\9 + \/ 93 / 2 *\/ 3 *\9 + \/ 93 / | \/ 12 *\/ 9 + \/ 93 \/ 2 *3 2 *\/ 3 *\/ 9 + \/ 93 ||||
/ _____________________________________\ / _____________________________________\ | _________________________________________________________________________________ | |- ---------- - ---------------------- + -------------------------- 12*|- ---------------------- - ----------------- + --------------------------||| _________________________________________________________________________________ | |- ---------- - ---------------------- + -------------------------- 12*|- ---------------------- - ----------------- + --------------------------|||| | _________________________________________________________________________________ | |- ---------- - ---------------------- + -------------------------- 12*|- ---------------------- - ----------------- + --------------------------||| _________________________________________________________________________________ | |- ---------- - ---------------------- + -------------------------- 12*|- ---------------------- - ----------------- + --------------------------|||| | _________________________________________________________________________________ | |- ---------- - ---------------------- + -------------------------- 12*|- ---------------------- - ----------------- + --------------------------||| _________________________________________________________________________________ | |- ---------- - ---------------------- + -------------------------- 12*|- ---------------------- - ----------------- + --------------------------|||| | _________________________________________________________________________________ | |- ---------- - ---------------------- + -------------------------- 12*|- ---------------------- - ----------------- + --------------------------||| _________________________________________________________________________________ | |- ---------- - ---------------------- + -------------------------- 12*|- ---------------------- - ----------------- + --------------------------||||
| / 2/3 | | / 2/3 | | / 2/3 2/3 | | 3 12 4 | 24 ____________ 8 ||| / 2/3 2/3 | | 3 12 4 | 24 ____________ 8 |||| | / 2/3 2/3 | | 3 12 4 | 24 ____________ 8 ||| / 2/3 2/3 | | 3 12 4 | 24 ____________ 8 |||| | / 2/3 2/3 | | 3 12 4 | 24 ____________ 8 ||| / 2/3 2/3 | | 3 12 4 | 24 ____________ 8 |||| | / 2/3 2/3 | | 3 12 4 | 24 ____________ 8 ||| / 2/3 2/3 | | 3 12 4 | 24 ____________ 8 ||||
| ___ / 3 ____ 3 ____ / ____\ | | ___ / 3 ____ 3 ____ / ____\ | | / 3 ____ / ____\ 2/3 3 ___ 3 ___ 2/3 / ____\ | | | 3 / ____ ||| / 3 ____ / ____\ 2/3 3 ___ 3 ___ 2/3 / ____\ | | | 3 / ____ |||| | / 3 ____ / ____\ 2/3 3 ___ 3 ___ 2/3 / ____\ | | | 3 / ____ ||| / 3 ____ / ____\ 2/3 3 ___ 3 ___ 2/3 / ____\ | | | 3 / ____ |||| | / 3 ____ / ____\ 2/3 3 ___ 3 ___ 2/3 / ____\ | | | 3 / ____ ||| / 3 ____ / ____\ 2/3 3 ___ 3 ___ 2/3 / ____\ | | | 3 / ____ |||| | / 3 ____ / ____\ 2/3 3 ___ 3 ___ 2/3 / ____\ | | | 3 / ____ ||| / 3 ____ / ____\ 2/3 3 ___ 3 ___ 2/3 / ____\ | | | 3 / ____ ||||
| I*\/ 6 *\/ - 2*\/ 18 + \/ 12 *\9 + \/ 93 / | | I*\/ 6 *\/ - 2*\/ 18 + \/ 12 *\9 + \/ 93 / | | / 1 5*\/ 18 *\9 + \/ 93 / 2 *\/ 3 7*\/ 2 *3 *\9 + \/ 93 / | \ \ 6*\/ 9 + \/ 93 //| / 1 5*\/ 18 *\9 + \/ 93 / 2 *\/ 3 7*\/ 2 *3 *\9 + \/ 93 / | \ \ 6*\/ 9 + \/ 93 //|| | / 1 5*\/ 18 *\9 + \/ 93 / 2 *\/ 3 7*\/ 2 *3 *\9 + \/ 93 / | \ \ 6*\/ 9 + \/ 93 //| / 1 5*\/ 18 *\9 + \/ 93 / 2 *\/ 3 7*\/ 2 *3 *\9 + \/ 93 / | \ \ 6*\/ 9 + \/ 93 //|| | / 1 5*\/ 18 *\9 + \/ 93 / 2 *\/ 3 7*\/ 2 *3 *\9 + \/ 93 / | \ \ 6*\/ 9 + \/ 93 //| / 1 5*\/ 18 *\9 + \/ 93 / 2 *\/ 3 7*\/ 2 *3 *\9 + \/ 93 / | \ \ 6*\/ 9 + \/ 93 //|| | / 1 5*\/ 18 *\9 + \/ 93 / 2 *\/ 3 7*\/ 2 *3 *\9 + \/ 93 / | \ \ 6*\/ 9 + \/ 93 //| / 1 5*\/ 18 *\9 + \/ 93 / 2 *\/ 3 7*\/ 2 *3 *\9 + \/ 93 / | \ \ 6*\/ 9 + \/ 93 //||
|x + -------------------------------------------------|*|x - -------------------------------------------------|*|x + / - - ------------------------ + ----------------- + ---------------------------- *cos|---------------------------------------------------------------------------------------------------------------------------------------------------------| + I* / - - ------------------------ + ----------------- + ---------------------------- *sin|---------------------------------------------------------------------------------------------------------------------------------------------------------||*|x + / - - ------------------------ + ----------------- + ---------------------------- *cos|---------------------------------------------------------------------------------------------------------------------------------------------------------| - I* / - - ------------------------ + ----------------- + ---------------------------- *sin|---------------------------------------------------------------------------------------------------------------------------------------------------------||*|x + - / - - ------------------------ + ----------------- + ---------------------------- *cos|---------------------------------------------------------------------------------------------------------------------------------------------------------| + I* / - - ------------------------ + ----------------- + ---------------------------- *sin|---------------------------------------------------------------------------------------------------------------------------------------------------------||*|x + - / - - ------------------------ + ----------------- + ---------------------------- *cos|---------------------------------------------------------------------------------------------------------------------------------------------------------| - I* / - - ------------------------ + ----------------- + ---------------------------- *sin|---------------------------------------------------------------------------------------------------------------------------------------------------------||
| ____________ | | ____________ | | / 3 288 2/3 96 \ 2 / / 3 288 2/3 96 \ 2 /| | / 3 288 2/3 96 \ 2 / / 3 288 2/3 96 \ 2 /| | / 3 288 2/3 96 \ 2 / / 3 288 2/3 96 \ 2 /| | / 3 288 2/3 96 \ 2 / / 3 288 2/3 96 \ 2 /|
| 6 / ____ | | 6 / ____ | | 4 / / ____\ 4 / / ____\ | | 4 / / ____\ 4 / / ____\ | | 4 / / ____\ 4 / / ____\ | | 4 / / ____\ 4 / / ____\ |
\ 6*\/ 9 + \/ 93 / \ 6*\/ 9 + \/ 93 / \ \/ 3*\9 + \/ 93 / \/ 3*\9 + \/ 93 / / \ \/ 3*\9 + \/ 93 / \/ 3*\9 + \/ 93 / / \ \/ 3*\9 + \/ 93 / \/ 3*\9 + \/ 93 / / \ \/ 3*\9 + \/ 93 / \/ 3*\9 + \/ 93 / /
$$\left(x - \frac{\sqrt{6} i \sqrt{- 2 \sqrt[3]{18} + \sqrt[3]{12} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}}{6 \sqrt[6]{9 + \sqrt{93}}}\right) \left(x + \frac{\sqrt{6} i \sqrt{- 2 \sqrt[3]{18} + \sqrt[3]{12} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}}{6 \sqrt[6]{9 + \sqrt{93}}}\right) \left(x + \left(\sqrt[4]{- \frac{5 \sqrt[3]{18} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{288} + \frac{2^{\frac{2}{3}} \sqrt[3]{3}}{3 \left(9 + \sqrt{93}\right)^{\frac{2}{3}}} + \frac{1}{3} + \frac{7 \sqrt[3]{2} \cdot 3^{\frac{2}{3}} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{96}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[3]{2} \sqrt[6]{3}}{- \frac{\sqrt[3]{12} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{12} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{3} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{4}} + \frac{2^{\frac{2}{3}} \cdot 3^{\frac{5}{6}} \sqrt[3]{9 + \sqrt{93}}}{12 \left(- \frac{\sqrt[3]{12} \sqrt[3]{9 + \sqrt{93}}}{24} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{6 \sqrt[3]{9 + \sqrt{93}}} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \sqrt[3]{9 + \sqrt{93}}}{8}\right)} \right)}}{2} \right)} + i \sqrt[4]{- \frac{5 \sqrt[3]{18} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{288} + \frac{2^{\frac{2}{3}} \sqrt[3]{3}}{3 \left(9 + \sqrt{93}\right)^{\frac{2}{3}}} + \frac{1}{3} + \frac{7 \sqrt[3]{2} \cdot 3^{\frac{2}{3}} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{96}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[3]{2} \sqrt[6]{3}}{- \frac{\sqrt[3]{12} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{12} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{3} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{4}} + \frac{2^{\frac{2}{3}} \cdot 3^{\frac{5}{6}} \sqrt[3]{9 + \sqrt{93}}}{12 \left(- \frac{\sqrt[3]{12} \sqrt[3]{9 + \sqrt{93}}}{24} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{6 \sqrt[3]{9 + \sqrt{93}}} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \sqrt[3]{9 + \sqrt{93}}}{8}\right)} \right)}}{2} \right)}\right)\right) \left(x + \left(\sqrt[4]{- \frac{5 \sqrt[3]{18} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{288} + \frac{2^{\frac{2}{3}} \sqrt[3]{3}}{3 \left(9 + \sqrt{93}\right)^{\frac{2}{3}}} + \frac{1}{3} + \frac{7 \sqrt[3]{2} \cdot 3^{\frac{2}{3}} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{96}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[3]{2} \sqrt[6]{3}}{- \frac{\sqrt[3]{12} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{12} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{3} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{4}} + \frac{2^{\frac{2}{3}} \cdot 3^{\frac{5}{6}} \sqrt[3]{9 + \sqrt{93}}}{12 \left(- \frac{\sqrt[3]{12} \sqrt[3]{9 + \sqrt{93}}}{24} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{6 \sqrt[3]{9 + \sqrt{93}}} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \sqrt[3]{9 + \sqrt{93}}}{8}\right)} \right)}}{2} \right)} - i \sqrt[4]{- \frac{5 \sqrt[3]{18} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{288} + \frac{2^{\frac{2}{3}} \sqrt[3]{3}}{3 \left(9 + \sqrt{93}\right)^{\frac{2}{3}}} + \frac{1}{3} + \frac{7 \sqrt[3]{2} \cdot 3^{\frac{2}{3}} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{96}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[3]{2} \sqrt[6]{3}}{- \frac{\sqrt[3]{12} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{12} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{3} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{4}} + \frac{2^{\frac{2}{3}} \cdot 3^{\frac{5}{6}} \sqrt[3]{9 + \sqrt{93}}}{12 \left(- \frac{\sqrt[3]{12} \sqrt[3]{9 + \sqrt{93}}}{24} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{6 \sqrt[3]{9 + \sqrt{93}}} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \sqrt[3]{9 + \sqrt{93}}}{8}\right)} \right)}}{2} \right)}\right)\right) \left(x + \left(- \sqrt[4]{- \frac{5 \sqrt[3]{18} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{288} + \frac{2^{\frac{2}{3}} \sqrt[3]{3}}{3 \left(9 + \sqrt{93}\right)^{\frac{2}{3}}} + \frac{1}{3} + \frac{7 \sqrt[3]{2} \cdot 3^{\frac{2}{3}} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{96}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[3]{2} \sqrt[6]{3}}{- \frac{\sqrt[3]{12} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{12} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{3} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{4}} + \frac{2^{\frac{2}{3}} \cdot 3^{\frac{5}{6}} \sqrt[3]{9 + \sqrt{93}}}{12 \left(- \frac{\sqrt[3]{12} \sqrt[3]{9 + \sqrt{93}}}{24} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{6 \sqrt[3]{9 + \sqrt{93}}} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \sqrt[3]{9 + \sqrt{93}}}{8}\right)} \right)}}{2} \right)} + i \sqrt[4]{- \frac{5 \sqrt[3]{18} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{288} + \frac{2^{\frac{2}{3}} \sqrt[3]{3}}{3 \left(9 + \sqrt{93}\right)^{\frac{2}{3}}} + \frac{1}{3} + \frac{7 \sqrt[3]{2} \cdot 3^{\frac{2}{3}} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{96}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[3]{2} \sqrt[6]{3}}{- \frac{\sqrt[3]{12} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{12} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{3} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{4}} + \frac{2^{\frac{2}{3}} \cdot 3^{\frac{5}{6}} \sqrt[3]{9 + \sqrt{93}}}{12 \left(- \frac{\sqrt[3]{12} \sqrt[3]{9 + \sqrt{93}}}{24} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{6 \sqrt[3]{9 + \sqrt{93}}} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \sqrt[3]{9 + \sqrt{93}}}{8}\right)} \right)}}{2} \right)}\right)\right) \left(x + \left(- \sqrt[4]{- \frac{5 \sqrt[3]{18} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{288} + \frac{2^{\frac{2}{3}} \sqrt[3]{3}}{3 \left(9 + \sqrt{93}\right)^{\frac{2}{3}}} + \frac{1}{3} + \frac{7 \sqrt[3]{2} \cdot 3^{\frac{2}{3}} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{96}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[3]{2} \sqrt[6]{3}}{- \frac{\sqrt[3]{12} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{12} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{3} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{4}} + \frac{2^{\frac{2}{3}} \cdot 3^{\frac{5}{6}} \sqrt[3]{9 + \sqrt{93}}}{12 \left(- \frac{\sqrt[3]{12} \sqrt[3]{9 + \sqrt{93}}}{24} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{6 \sqrt[3]{9 + \sqrt{93}}} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \sqrt[3]{9 + \sqrt{93}}}{8}\right)} \right)}}{2} \right)} - i \sqrt[4]{- \frac{5 \sqrt[3]{18} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{288} + \frac{2^{\frac{2}{3}} \sqrt[3]{3}}{3 \left(9 + \sqrt{93}\right)^{\frac{2}{3}}} + \frac{1}{3} + \frac{7 \sqrt[3]{2} \cdot 3^{\frac{2}{3}} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{96}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt[3]{2} \sqrt[6]{3}}{- \frac{\sqrt[3]{12} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{12} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{3} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \left(9 + \sqrt{93}\right)^{\frac{2}{3}}}{4}} + \frac{2^{\frac{2}{3}} \cdot 3^{\frac{5}{6}} \sqrt[3]{9 + \sqrt{93}}}{12 \left(- \frac{\sqrt[3]{12} \sqrt[3]{9 + \sqrt{93}}}{24} - \frac{\sqrt[3]{2} \cdot 3^{\frac{2}{3}}}{6 \sqrt[3]{9 + \sqrt{93}}} + \frac{2^{\frac{2}{3}} \sqrt[3]{3} \sqrt[3]{9 + \sqrt{93}}}{8}\right)} \right)}}{2} \right)}\right)\right)$$
(((((x + i*sqrt(6)*sqrt(-2*18^(1/3) + 12^(1/3)*(9 + sqrt(93))^(2/3))/(6*(9 + sqrt(93))^(1/6)))*(x - i*sqrt(6)*sqrt(-2*18^(1/3) + 12^(1/3)*(9 + sqrt(93))^(2/3))/(6*(9 + sqrt(93))^(1/6))))*(x + (1/3 - 5*18^(1/3)*(9 + sqrt(93))^(2/3)/288 + 2^(2/3)*3^(1/3)/(3*(9 + sqrt(93))^(2/3)) + 7*2^(1/3)*3^(2/3)*(9 + sqrt(93))^(2/3)/96)^(1/4)*cos(atan(2^(1/3)*3^(1/6)/(-2^(1/3)*3^(2/3)/3 - 12^(1/3)*(9 + sqrt(93))^(2/3)/12 + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(2/3)/4) + 2^(2/3)*3^(5/6)*(9 + sqrt(93))^(1/3)/(12*(-12^(1/3)*(9 + sqrt(93))^(1/3)/24 - 2^(1/3)*3^(2/3)/(6*(9 + sqrt(93))^(1/3)) + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(1/3)/8)))/2) + i*(1/3 - 5*18^(1/3)*(9 + sqrt(93))^(2/3)/288 + 2^(2/3)*3^(1/3)/(3*(9 + sqrt(93))^(2/3)) + 7*2^(1/3)*3^(2/3)*(9 + sqrt(93))^(2/3)/96)^(1/4)*sin(atan(2^(1/3)*3^(1/6)/(-2^(1/3)*3^(2/3)/3 - 12^(1/3)*(9 + sqrt(93))^(2/3)/12 + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(2/3)/4) + 2^(2/3)*3^(5/6)*(9 + sqrt(93))^(1/3)/(12*(-12^(1/3)*(9 + sqrt(93))^(1/3)/24 - 2^(1/3)*3^(2/3)/(6*(9 + sqrt(93))^(1/3)) + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(1/3)/8)))/2)))*(x + (1/3 - 5*18^(1/3)*(9 + sqrt(93))^(2/3)/288 + 2^(2/3)*3^(1/3)/(3*(9 + sqrt(93))^(2/3)) + 7*2^(1/3)*3^(2/3)*(9 + sqrt(93))^(2/3)/96)^(1/4)*cos(atan(2^(1/3)*3^(1/6)/(-2^(1/3)*3^(2/3)/3 - 12^(1/3)*(9 + sqrt(93))^(2/3)/12 + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(2/3)/4) + 2^(2/3)*3^(5/6)*(9 + sqrt(93))^(1/3)/(12*(-12^(1/3)*(9 + sqrt(93))^(1/3)/24 - 2^(1/3)*3^(2/3)/(6*(9 + sqrt(93))^(1/3)) + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(1/3)/8)))/2) - i*(1/3 - 5*18^(1/3)*(9 + sqrt(93))^(2/3)/288 + 2^(2/3)*3^(1/3)/(3*(9 + sqrt(93))^(2/3)) + 7*2^(1/3)*3^(2/3)*(9 + sqrt(93))^(2/3)/96)^(1/4)*sin(atan(2^(1/3)*3^(1/6)/(-2^(1/3)*3^(2/3)/3 - 12^(1/3)*(9 + sqrt(93))^(2/3)/12 + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(2/3)/4) + 2^(2/3)*3^(5/6)*(9 + sqrt(93))^(1/3)/(12*(-12^(1/3)*(9 + sqrt(93))^(1/3)/24 - 2^(1/3)*3^(2/3)/(6*(9 + sqrt(93))^(1/3)) + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(1/3)/8)))/2)))*(x - (1/3 - 5*18^(1/3)*(9 + sqrt(93))^(2/3)/288 + 2^(2/3)*3^(1/3)/(3*(9 + sqrt(93))^(2/3)) + 7*2^(1/3)*3^(2/3)*(9 + sqrt(93))^(2/3)/96)^(1/4)*cos(atan(2^(1/3)*3^(1/6)/(-2^(1/3)*3^(2/3)/3 - 12^(1/3)*(9 + sqrt(93))^(2/3)/12 + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(2/3)/4) + 2^(2/3)*3^(5/6)*(9 + sqrt(93))^(1/3)/(12*(-12^(1/3)*(9 + sqrt(93))^(1/3)/24 - 2^(1/3)*3^(2/3)/(6*(9 + sqrt(93))^(1/3)) + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(1/3)/8)))/2) + i*(1/3 - 5*18^(1/3)*(9 + sqrt(93))^(2/3)/288 + 2^(2/3)*3^(1/3)/(3*(9 + sqrt(93))^(2/3)) + 7*2^(1/3)*3^(2/3)*(9 + sqrt(93))^(2/3)/96)^(1/4)*sin(atan(2^(1/3)*3^(1/6)/(-2^(1/3)*3^(2/3)/3 - 12^(1/3)*(9 + sqrt(93))^(2/3)/12 + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(2/3)/4) + 2^(2/3)*3^(5/6)*(9 + sqrt(93))^(1/3)/(12*(-12^(1/3)*(9 + sqrt(93))^(1/3)/24 - 2^(1/3)*3^(2/3)/(6*(9 + sqrt(93))^(1/3)) + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(1/3)/8)))/2)))*(x - (1/3 - 5*18^(1/3)*(9 + sqrt(93))^(2/3)/288 + 2^(2/3)*3^(1/3)/(3*(9 + sqrt(93))^(2/3)) + 7*2^(1/3)*3^(2/3)*(9 + sqrt(93))^(2/3)/96)^(1/4)*cos(atan(2^(1/3)*3^(1/6)/(-2^(1/3)*3^(2/3)/3 - 12^(1/3)*(9 + sqrt(93))^(2/3)/12 + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(2/3)/4) + 2^(2/3)*3^(5/6)*(9 + sqrt(93))^(1/3)/(12*(-12^(1/3)*(9 + sqrt(93))^(1/3)/24 - 2^(1/3)*3^(2/3)/(6*(9 + sqrt(93))^(1/3)) + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(1/3)/8)))/2) - i*(1/3 - 5*18^(1/3)*(9 + sqrt(93))^(2/3)/288 + 2^(2/3)*3^(1/3)/(3*(9 + sqrt(93))^(2/3)) + 7*2^(1/3)*3^(2/3)*(9 + sqrt(93))^(2/3)/96)^(1/4)*sin(atan(2^(1/3)*3^(1/6)/(-2^(1/3)*3^(2/3)/3 - 12^(1/3)*(9 + sqrt(93))^(2/3)/12 + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(2/3)/4) + 2^(2/3)*3^(5/6)*(9 + sqrt(93))^(1/3)/(12*(-12^(1/3)*(9 + sqrt(93))^(1/3)/24 - 2^(1/3)*3^(2/3)/(6*(9 + sqrt(93))^(1/3)) + 2^(2/3)*3^(1/3)*(9 + sqrt(93))^(1/3)/8)))/2))
Unión de expresiones racionales
[src]
2 / 4\ 1 + x *\1 + x /
$$x^{2} \left(x^{4} + 1\right) + 1$$
1 + x^2*(1 + x^4)