(x-1)^2*(x-5)-6-9*(x-5)-2*(x+1)=0 la ecuación
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Solución
/ 1 \ / / _____\\ / / 1 \ / / _____\\ / / _____\\\ / / _____\\
49*re|--------------------------------------| | |12*\/ 762 || | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 ||| | |12*\/ 762 ||
| ___________________ / ___\| |atan|----------|| | | ___________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------||
|3 / _____ | 1 I*\/ 3 || | \ 89 /| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /|| ___ | \ 89 /|
|\/ 89 + 12*I*\/ 762 *|- - - -------|| 7*cos|----------------| | |\/ 89 + 12*I*\/ 762 *|- - - -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------|
7 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 /
x1 = - - --------------------------------------------- + ----------------------- + I*|- --------------------------------------------- + ----------------------- + -----------------------------| - -----------------------------
3 3 6 \ 3 6 6 / 6
x 1 = − 7 3 sin ( atan ( 12 762 89 ) 3 ) 6 − 49 re ( 1 ( − 1 2 − 3 i 2 ) 89 + 12 762 i 3 ) 3 + 7 cos ( atan ( 12 762 89 ) 3 ) 6 + 7 3 + i ( − 49 im ( 1 ( − 1 2 − 3 i 2 ) 89 + 12 762 i 3 ) 3 + 7 sin ( atan ( 12 762 89 ) 3 ) 6 + 7 3 cos ( atan ( 12 762 89 ) 3 ) 6 ) x_{1} = - \frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7}{3} + i \left(- \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6}\right) x 1 = − 6 7 3 sin ( 3 atan ( 89 12 762 ) ) − 3 49 re ( ( − 2 1 − 2 3 i ) 3 89 + 12 762 i 1 ) + 6 7 cos ( 3 atan ( 89 12 762 ) ) + 3 7 + i − 3 49 im ( ( − 2 1 − 2 3 i ) 3 89 + 12 762 i 1 ) + 6 7 sin ( 3 atan ( 89 12 762 ) ) + 6 7 3 cos ( 3 atan ( 89 12 762 ) )
/ 1 \ / / _____\\ / / 1 \ / / _____\\ / / _____\\\ / / _____\\
49*re|--------------------------------------| | |12*\/ 762 || | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 ||| | |12*\/ 762 ||
| ___________________ / ___\| |atan|----------|| | | ___________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------||
|3 / _____ | 1 I*\/ 3 || | \ 89 /| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /|| ___ | \ 89 /|
|\/ 89 + 12*I*\/ 762 *|- - + -------|| 7*cos|----------------| | |\/ 89 + 12*I*\/ 762 *|- - + -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------|
7 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 /
x2 = - - --------------------------------------------- + ----------------------- + I*|- --------------------------------------------- + ----------------------- - -----------------------------| + -----------------------------
3 3 6 \ 3 6 6 / 6
x 2 = 7 3 sin ( atan ( 12 762 89 ) 3 ) 6 + 7 cos ( atan ( 12 762 89 ) 3 ) 6 − 49 re ( 1 ( − 1 2 + 3 i 2 ) 89 + 12 762 i 3 ) 3 + 7 3 + i ( − 7 3 cos ( atan ( 12 762 89 ) 3 ) 6 + 7 sin ( atan ( 12 762 89 ) 3 ) 6 − 49 im ( 1 ( − 1 2 + 3 i 2 ) 89 + 12 762 i 3 ) 3 ) x_{2} = \frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7}{3} + i \left(- \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3}\right) x 2 = 6 7 3 sin ( 3 atan ( 89 12 762 ) ) + 6 7 cos ( 3 atan ( 89 12 762 ) ) − 3 49 re ( ( − 2 1 + 2 3 i ) 3 89 + 12 762 i 1 ) + 3 7 + i − 6 7 3 cos ( 3 atan ( 89 12 762 ) ) + 6 7 sin ( 3 atan ( 89 12 762 ) ) − 3 49 im ( ( − 2 1 + 2 3 i ) 3 89 + 12 762 i 1 )
___________________
3 / _____
7 49 \/ 89 + 12*I*\/ 762
x3 = - - ------------------------ - ----------------------
3 ___________________ 3
3 / _____
3*\/ 89 + 12*I*\/ 762
x 3 = 7 3 − 89 + 12 762 i 3 3 − 49 3 89 + 12 762 i 3 x_{3} = \frac{7}{3} - \frac{\sqrt[3]{89 + 12 \sqrt{762} i}}{3} - \frac{49}{3 \sqrt[3]{89 + 12 \sqrt{762} i}} x 3 = 3 7 − 3 3 89 + 12 762 i − 3 3 89 + 12 762 i 49
x3 = 7/3 - (89 + 12*sqrt(762)*i)^(1/3)/3 - 49/(3*(89 + 12*sqrt(762)*i)^(1/3))
Suma y producto de raíces
[src]
/ 1 \ / / _____\\ / / 1 \ / / _____\\ / / _____\\\ / / _____\\ / 1 \ / / _____\\ / / 1 \ / / _____\\ / / _____\\\ / / _____\\
49*re|--------------------------------------| | |12*\/ 762 || | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 ||| | |12*\/ 762 || 49*re|--------------------------------------| | |12*\/ 762 || | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 ||| | |12*\/ 762 ||
| ___________________ / ___\| |atan|----------|| | | ___________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------|| | ___________________ / ___\| |atan|----------|| | | ___________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------||
|3 / _____ | 1 I*\/ 3 || | \ 89 /| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /|| ___ | \ 89 /| |3 / _____ | 1 I*\/ 3 || | \ 89 /| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /|| ___ | \ 89 /| ___________________
|\/ 89 + 12*I*\/ 762 *|- - - -------|| 7*cos|----------------| | |\/ 89 + 12*I*\/ 762 *|- - - -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------| |\/ 89 + 12*I*\/ 762 *|- - + -------|| 7*cos|----------------| | |\/ 89 + 12*I*\/ 762 *|- - + -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------| 3 / _____
7 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 / 7 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 / 7 49 \/ 89 + 12*I*\/ 762
- - --------------------------------------------- + ----------------------- + I*|- --------------------------------------------- + ----------------------- + -----------------------------| - ----------------------------- + - - --------------------------------------------- + ----------------------- + I*|- --------------------------------------------- + ----------------------- - -----------------------------| + ----------------------------- + - - ------------------------ - ----------------------
3 3 6 \ 3 6 6 / 6 3 3 6 \ 3 6 6 / 6 3 ___________________ 3
3 / _____
3*\/ 89 + 12*I*\/ 762
( 7 3 − 89 + 12 762 i 3 3 − 49 3 89 + 12 762 i 3 ) + ( ( 7 3 sin ( atan ( 12 762 89 ) 3 ) 6 + 7 cos ( atan ( 12 762 89 ) 3 ) 6 − 49 re ( 1 ( − 1 2 + 3 i 2 ) 89 + 12 762 i 3 ) 3 + 7 3 + i ( − 7 3 cos ( atan ( 12 762 89 ) 3 ) 6 + 7 sin ( atan ( 12 762 89 ) 3 ) 6 − 49 im ( 1 ( − 1 2 + 3 i 2 ) 89 + 12 762 i 3 ) 3 ) ) + ( − 7 3 sin ( atan ( 12 762 89 ) 3 ) 6 − 49 re ( 1 ( − 1 2 − 3 i 2 ) 89 + 12 762 i 3 ) 3 + 7 cos ( atan ( 12 762 89 ) 3 ) 6 + 7 3 + i ( − 49 im ( 1 ( − 1 2 − 3 i 2 ) 89 + 12 762 i 3 ) 3 + 7 sin ( atan ( 12 762 89 ) 3 ) 6 + 7 3 cos ( atan ( 12 762 89 ) 3 ) 6 ) ) ) \left(\frac{7}{3} - \frac{\sqrt[3]{89 + 12 \sqrt{762} i}}{3} - \frac{49}{3 \sqrt[3]{89 + 12 \sqrt{762} i}}\right) + \left(\left(\frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7}{3} + i \left(- \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3}\right)\right) + \left(- \frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7}{3} + i \left(- \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6}\right)\right)\right) ( 3 7 − 3 3 89 + 12 762 i − 3 3 89 + 12 762 i 49 ) + 6 7 3 sin ( 3 atan ( 89 12 762 ) ) + 6 7 cos ( 3 atan ( 89 12 762 ) ) − 3 49 re ( ( − 2 1 + 2 3 i ) 3 89 + 12 762 i 1 ) + 3 7 + i − 6 7 3 cos ( 3 atan ( 89 12 762 ) ) + 6 7 sin ( 3 atan ( 89 12 762 ) ) − 3 49 im ( ( − 2 1 + 2 3 i ) 3 89 + 12 762 i 1 ) + − 6 7 3 sin ( 3 atan ( 89 12 762 ) ) − 3 49 re ( ( − 2 1 − 2 3 i ) 3 89 + 12 762 i 1 ) + 6 7 cos ( 3 atan ( 89 12 762 ) ) + 3 7 + i − 3 49 im ( ( − 2 1 − 2 3 i ) 3 89 + 12 762 i 1 ) + 6 7 sin ( 3 atan ( 89 12 762 ) ) + 6 7 3 cos ( 3 atan ( 89 12 762 ) )
/ 1 \ / 1 \ / / _____\\ / / 1 \ / / _____\\ / / _____\\\ / / 1 \ / / _____\\ / / _____\\\
49*re|--------------------------------------| 49*re|--------------------------------------| | |12*\/ 762 || | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 ||| | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 |||
| ___________________ / ___\| | ___________________ / ___\| |atan|----------|| | | ___________________ / ___\| |atan|----------|| |atan|----------||| | | ___________________ / ___\| |atan|----------|| |atan|----------|||
|3 / _____ | 1 I*\/ 3 || |3 / _____ | 1 I*\/ 3 || ___________________ | \ 89 /| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /|| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /||
|\/ 89 + 12*I*\/ 762 *|- - + -------|| |\/ 89 + 12*I*\/ 762 *|- - - -------|| 3 / _____ 7*cos|----------------| | |\/ 89 + 12*I*\/ 762 *|- - + -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| | |\/ 89 + 12*I*\/ 762 *|- - - -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------||
49 \ \ 2 2 // \ \ 2 2 // \/ 89 + 12*I*\/ 762 \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| | \ \ 2 2 // \ 3 / \ 3 /|
7 - ------------------------ - --------------------------------------------- - --------------------------------------------- - ---------------------- + ----------------------- + I*|- --------------------------------------------- + ----------------------- - -----------------------------| + I*|- --------------------------------------------- + ----------------------- + -----------------------------|
___________________ 3 3 3 3 \ 3 6 6 / \ 3 6 6 /
3 / _____
3*\/ 89 + 12*I*\/ 762
− 49 re ( 1 ( − 1 2 − 3 i 2 ) 89 + 12 762 i 3 ) 3 − 49 re ( 1 ( − 1 2 + 3 i 2 ) 89 + 12 762 i 3 ) 3 + 7 cos ( atan ( 12 762 89 ) 3 ) 3 + 7 − 89 + 12 762 i 3 3 + i ( − 49 im ( 1 ( − 1 2 − 3 i 2 ) 89 + 12 762 i 3 ) 3 + 7 sin ( atan ( 12 762 89 ) 3 ) 6 + 7 3 cos ( atan ( 12 762 89 ) 3 ) 6 ) + i ( − 7 3 cos ( atan ( 12 762 89 ) 3 ) 6 + 7 sin ( atan ( 12 762 89 ) 3 ) 6 − 49 im ( 1 ( − 1 2 + 3 i 2 ) 89 + 12 762 i 3 ) 3 ) − 49 3 89 + 12 762 i 3 - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{3} + 7 - \frac{\sqrt[3]{89 + 12 \sqrt{762} i}}{3} + i \left(- \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6}\right) + i \left(- \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3}\right) - \frac{49}{3 \sqrt[3]{89 + 12 \sqrt{762} i}} − 3 49 re ( ( − 2 1 − 2 3 i ) 3 89 + 12 762 i 1 ) − 3 49 re ( ( − 2 1 + 2 3 i ) 3 89 + 12 762 i 1 ) + 3 7 cos ( 3 atan ( 89 12 762 ) ) + 7 − 3 3 89 + 12 762 i + i − 3 49 im ( ( − 2 1 − 2 3 i ) 3 89 + 12 762 i 1 ) + 6 7 sin ( 3 atan ( 89 12 762 ) ) + 6 7 3 cos ( 3 atan ( 89 12 762 ) ) + i − 6 7 3 cos ( 3 atan ( 89 12 762 ) ) + 6 7 sin ( 3 atan ( 89 12 762 ) ) − 3 49 im ( ( − 2 1 + 2 3 i ) 3 89 + 12 762 i 1 ) − 3 3 89 + 12 762 i 49
/ / 1 \ / / _____\\ / / 1 \ / / _____\\ / / _____\\\ / / _____\\\ / / 1 \ / / _____\\ / / 1 \ / / _____\\ / / _____\\\ / / _____\\\
| 49*re|--------------------------------------| | |12*\/ 762 || | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 ||| | |12*\/ 762 ||| | 49*re|--------------------------------------| | |12*\/ 762 || | 49*im|--------------------------------------| | |12*\/ 762 || | |12*\/ 762 ||| | |12*\/ 762 |||
| | ___________________ / ___\| |atan|----------|| | | ___________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------||| | | ___________________ / ___\| |atan|----------|| | | ___________________ / ___\| |atan|----------|| |atan|----------||| |atan|----------|||
| |3 / _____ | 1 I*\/ 3 || | \ 89 /| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /|| ___ | \ 89 /|| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| | |3 / _____ | 1 I*\/ 3 || | \ 89 /| ___ | \ 89 /|| ___ | \ 89 /|| / ___________________\
| |\/ 89 + 12*I*\/ 762 *|- - - -------|| 7*cos|----------------| | |\/ 89 + 12*I*\/ 762 *|- - - -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------|| | |\/ 89 + 12*I*\/ 762 *|- - + -------|| 7*cos|----------------| | |\/ 89 + 12*I*\/ 762 *|- - + -------|| 7*sin|----------------| 7*\/ 3 *cos|----------------|| 7*\/ 3 *sin|----------------|| | 3 / _____ |
|7 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 /| |7 \ \ 2 2 // \ 3 / | \ \ 2 2 // \ 3 / \ 3 /| \ 3 /| |7 49 \/ 89 + 12*I*\/ 762 |
|- - --------------------------------------------- + ----------------------- + I*|- --------------------------------------------- + ----------------------- + -----------------------------| - -----------------------------|*|- - --------------------------------------------- + ----------------------- + I*|- --------------------------------------------- + ----------------------- - -----------------------------| + -----------------------------|*|- - ------------------------ - ----------------------|
\3 3 6 \ 3 6 6 / 6 / \3 3 6 \ 3 6 6 / 6 / |3 ___________________ 3 |
| 3 / _____ |
\ 3*\/ 89 + 12*I*\/ 762 /
( − 7 3 sin ( atan ( 12 762 89 ) 3 ) 6 − 49 re ( 1 ( − 1 2 − 3 i 2 ) 89 + 12 762 i 3 ) 3 + 7 cos ( atan ( 12 762 89 ) 3 ) 6 + 7 3 + i ( − 49 im ( 1 ( − 1 2 − 3 i 2 ) 89 + 12 762 i 3 ) 3 + 7 sin ( atan ( 12 762 89 ) 3 ) 6 + 7 3 cos ( atan ( 12 762 89 ) 3 ) 6 ) ) ( 7 3 sin ( atan ( 12 762 89 ) 3 ) 6 + 7 cos ( atan ( 12 762 89 ) 3 ) 6 − 49 re ( 1 ( − 1 2 + 3 i 2 ) 89 + 12 762 i 3 ) 3 + 7 3 + i ( − 7 3 cos ( atan ( 12 762 89 ) 3 ) 6 + 7 sin ( atan ( 12 762 89 ) 3 ) 6 − 49 im ( 1 ( − 1 2 + 3 i 2 ) 89 + 12 762 i 3 ) 3 ) ) ( 7 3 − 89 + 12 762 i 3 3 − 49 3 89 + 12 762 i 3 ) \left(- \frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7}{3} + i \left(- \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6}\right)\right) \left(\frac{7 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3} + \frac{7}{3} + i \left(- \frac{7 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} + \frac{7 \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}}{6} - \frac{49 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{89 + 12 \sqrt{762} i}}\right)}}{3}\right)\right) \left(\frac{7}{3} - \frac{\sqrt[3]{89 + 12 \sqrt{762} i}}{3} - \frac{49}{3 \sqrt[3]{89 + 12 \sqrt{762} i}}\right) − 6 7 3 sin ( 3 atan ( 89 12 762 ) ) − 3 49 re ( ( − 2 1 − 2 3 i ) 3 89 + 12 762 i 1 ) + 6 7 cos ( 3 atan ( 89 12 762 ) ) + 3 7 + i − 3 49 im ( ( − 2 1 − 2 3 i ) 3 89 + 12 762 i 1 ) + 6 7 sin ( 3 atan ( 89 12 762 ) ) + 6 7 3 cos ( 3 atan ( 89 12 762 ) ) 6 7 3 sin ( 3 atan ( 89 12 762 ) ) + 6 7 cos ( 3 atan ( 89 12 762 ) ) − 3 49 re ( ( − 2 1 + 2 3 i ) 3 89 + 12 762 i 1 ) + 3 7 + i − 6 7 3 cos ( 3 atan ( 89 12 762 ) ) + 6 7 sin ( 3 atan ( 89 12 762 ) ) − 3 49 im ( ( − 2 1 + 2 3 i ) 3 89 + 12 762 i 1 ) ( 3 7 − 3 3 89 + 12 762 i − 3 3 89 + 12 762 i 49 )
/ / / _____\\ / / _____\\\
| | |12*\/ 762 || | |12*\/ 762 |||
/ ___________________ / ___________________\\ | |atan|----------|| |2*atan|----------|||
| 3 / _____ | 3 / _____ || | | \ 89 /| | \ 89 /||
-98*\49 - \/ 89 + 12*I*\/ 762 *\7 - \/ 89 + 12*I*\/ 762 //*|cos|----------------| + cos|------------------||
\ \ 3 / \ 3 //
----------------------------------------------------------------------------------------------------------------
___________________
3 / _____
27*\/ 89 + 12*I*\/ 762
− 98 ( 49 − ( 7 − 89 + 12 762 i 3 ) 89 + 12 762 i 3 ) ( cos ( 2 atan ( 12 762 89 ) 3 ) + cos ( atan ( 12 762 89 ) 3 ) ) 27 89 + 12 762 i 3 - \frac{98 \left(49 - \left(7 - \sqrt[3]{89 + 12 \sqrt{762} i}\right) \sqrt[3]{89 + 12 \sqrt{762} i}\right) \left(\cos{\left(\frac{2 \operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)} + \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{762}}{89} \right)}}{3} \right)}\right)}{27 \sqrt[3]{89 + 12 \sqrt{762} i}} − 27 3 89 + 12 762 i 98 ( 49 − ( 7 − 3 89 + 12 762 i ) 3 89 + 12 762 i ) ( cos ( 3 2 atan ( 89 12 762 ) ) + cos ( 3 atan ( 89 12 762 ) ) )
-98*(49 - (89 + 12*i*sqrt(762))^(1/3)*(7 - (89 + 12*i*sqrt(762))^(1/3)))*(cos(atan(12*sqrt(762)/89)/3) + cos(2*atan(12*sqrt(762)/89)/3))/(27*(89 + 12*i*sqrt(762))^(1/3))