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-x^3-x^2+161*x-80=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   3    2                 
- x  - x  + 161*x - 80 = 0
(161x+(−x3−x2))−80=0\left(161 x + \left(- x^{3} - x^{2}\right)\right) - 80 = 0
Simplificar
Teorema de Cardano-Vieta
reescribamos la ecuación
(161x+(−x3−x2))−80=0\left(161 x + \left(- x^{3} - x^{2}\right)\right) - 80 = 0
de
ax3+bx2+cx+d=0a x^{3} + b x^{2} + c x + d = 0
como ecuación cúbica reducida
x3+bx2a+cxa+da=0x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0
x3+x2−161x+80=0x^{3} + x^{2} - 161 x + 80 = 0
px2+qx+v+x3=0p x^{2} + q x + v + x^{3} = 0
donde
p=bap = \frac{b}{a}
p=1p = 1
q=caq = \frac{c}{a}
q=−161q = -161
v=dav = \frac{d}{a}
v=80v = 80
Fórmulas de Cardano-Vieta
x1+x2+x3=−px_{1} + x_{2} + x_{3} = - p
x1x2+x1x3+x2x3=qx_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q
x1x2x3=vx_{1} x_{2} x_{3} = v
x1+x2+x3=−1x_{1} + x_{2} + x_{3} = -1
x1x2+x1x3+x2x3=−161x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -161
x1x2x3=80x_{1} x_{2} x_{3} = 80
Respuesta rápida [src] 
                 /                      1                       \                                    /        /                      1                       \                                                                    \                                     
           484*re|----------------------------------------------|         /    /    __________\\     |  484*im|----------------------------------------------|         /    /    __________\\               /    /    __________\\|               /    /    __________\\
                 |                     _________________________|         |    |3*\/ 48942255 ||     |        |                     _________________________|         |    |3*\/ 48942255 ||               |    |3*\/ 48942255 |||               |    |3*\/ 48942255 ||
                 |/          ___\     /              __________ |         |atan|--------------||     |        |/          ___\     /              __________ |         |atan|--------------||               |atan|--------------|||               |atan|--------------||
                 ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |         |    \     3611     /|     |        ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |         |    \     3611     /|        ___    |    \     3611     /||        ___    |    \     3611     /|
                 ||- - - -------|*3 /   ---- + ---------------- |   11*cos|--------------------|     |        ||- - - -------|*3 /   ---- + ---------------- |   11*sin|--------------------|   11*\/ 3 *cos|--------------------||   11*\/ 3 *sin|--------------------|
       1         \\  2      2   / \/     2            2         /         \         3          /     |        \\  2      2   / \/     2            2         /         \         3          /               \         3          /|               \         3          /
x1 = - - - ------------------------------------------------------ + ---------------------------- + I*|- ------------------------------------------------------ + ---------------------------- + ----------------------------------| - ----------------------------------
       3                             3                                           3                   \                            3                                           3                                 3                 /                   3
x1=−113sin⁡(atan⁡(3489422553611)3)3−13−484re⁡(1(−12−3i2)36112+348942255i23)3+11cos⁡(atan⁡(3489422553611)3)3+i(−484im⁡(1(−12−3i2)36112+348942255i23)3+11sin⁡(atan⁡(3489422553611)3)3+113cos⁡(atan⁡(3489422553611)3)3)x_{1} = - \frac{11 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{1}{3} - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{11 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + i \left(- \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3}\right) 
                 /                      1                       \                                    /        /                      1                       \                                                                    \                                     
           484*re|----------------------------------------------|         /    /    __________\\     |  484*im|----------------------------------------------|         /    /    __________\\               /    /    __________\\|               /    /    __________\\
                 |                     _________________________|         |    |3*\/ 48942255 ||     |        |                     _________________________|         |    |3*\/ 48942255 ||               |    |3*\/ 48942255 |||               |    |3*\/ 48942255 ||
                 |/          ___\     /              __________ |         |atan|--------------||     |        |/          ___\     /              __________ |         |atan|--------------||               |atan|--------------|||               |atan|--------------||
                 ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |         |    \     3611     /|     |        ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |         |    \     3611     /|        ___    |    \     3611     /||        ___    |    \     3611     /|
                 ||- - + -------|*3 /   ---- + ---------------- |   11*cos|--------------------|     |        ||- - + -------|*3 /   ---- + ---------------- |   11*sin|--------------------|   11*\/ 3 *cos|--------------------||   11*\/ 3 *sin|--------------------|
       1         \\  2      2   / \/     2            2         /         \         3          /     |        \\  2      2   / \/     2            2         /         \         3          /               \         3          /|               \         3          /
x2 = - - - ------------------------------------------------------ + ---------------------------- + I*|- ------------------------------------------------------ + ---------------------------- - ----------------------------------| + ----------------------------------
       3                             3                                           3                   \                            3                                           3                                 3                 /                   3
x2=−13+113sin⁡(atan⁡(3489422553611)3)3+11cos⁡(atan⁡(3489422553611)3)3−484re⁡(1(−12+3i2)36112+348942255i23)3+i(−113cos⁡(atan⁡(3489422553611)3)3+11sin⁡(atan⁡(3489422553611)3)3−484im⁡(1(−12+3i2)36112+348942255i23)3)x_{2} = - \frac{1}{3} + \frac{11 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + i \left(- \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3}\right) 
                                                   _________________________
                                                  /              __________ 
                                                 /  3611   3*I*\/ 48942255  
                                              3 /   ---- + ---------------- 
       1                 484                  \/     2            2         
x3 = - - - -------------------------------- - ------------------------------
       3          _________________________                 3               
                 /              __________                                  
                /  3611   3*I*\/ 48942255                                   
           3*3 /   ---- + ----------------                                  
             \/     2            2
x3=−13−36112+348942255i233−484336112+348942255i23x_{3} = - \frac{1}{3} - \frac{\sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}{3} - \frac{484}{3 \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}} 
x3 = -1/3 - (3611/2 + 3*sqrt(48942255)*i/2)^(1/3)/3 - 484/(3*(3611/2 + 3*sqrt(48942255)*i/2)^(1/3))
Suma y producto de raíces [src] 
suma
            /                      1                       \                                    /        /                      1                       \                                                                    \                                                    /                      1                       \                                    /        /                      1                       \                                                                    \                                                                                                               
      484*re|----------------------------------------------|         /    /    __________\\     |  484*im|----------------------------------------------|         /    /    __________\\               /    /    __________\\|               /    /    __________\\         484*re|----------------------------------------------|         /    /    __________\\     |  484*im|----------------------------------------------|         /    /    __________\\               /    /    __________\\|               /    /    __________\\                                                                          
            |                     _________________________|         |    |3*\/ 48942255 ||     |        |                     _________________________|         |    |3*\/ 48942255 ||               |    |3*\/ 48942255 |||               |    |3*\/ 48942255 ||               |                     _________________________|         |    |3*\/ 48942255 ||     |        |                     _________________________|         |    |3*\/ 48942255 ||               |    |3*\/ 48942255 |||               |    |3*\/ 48942255 ||                                                 _________________________
            |/          ___\     /              __________ |         |atan|--------------||     |        |/          ___\     /              __________ |         |atan|--------------||               |atan|--------------|||               |atan|--------------||               |/          ___\     /              __________ |         |atan|--------------||     |        |/          ___\     /              __________ |         |atan|--------------||               |atan|--------------|||               |atan|--------------||                                                /              __________ 
            ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |         |    \     3611     /|     |        ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |         |    \     3611     /|        ___    |    \     3611     /||        ___    |    \     3611     /|               ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |         |    \     3611     /|     |        ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |         |    \     3611     /|        ___    |    \     3611     /||        ___    |    \     3611     /|                                               /  3611   3*I*\/ 48942255  
            ||- - - -------|*3 /   ---- + ---------------- |   11*cos|--------------------|     |        ||- - - -------|*3 /   ---- + ---------------- |   11*sin|--------------------|   11*\/ 3 *cos|--------------------||   11*\/ 3 *sin|--------------------|               ||- - + -------|*3 /   ---- + ---------------- |   11*cos|--------------------|     |        ||- - + -------|*3 /   ---- + ---------------- |   11*sin|--------------------|   11*\/ 3 *cos|--------------------||   11*\/ 3 *sin|--------------------|                                            3 /   ---- + ---------------- 
  1         \\  2      2   / \/     2            2         /         \         3          /     |        \\  2      2   / \/     2            2         /         \         3          /               \         3          /|               \         3          /     1         \\  2      2   / \/     2            2         /         \         3          /     |        \\  2      2   / \/     2            2         /         \         3          /               \         3          /|               \         3          /     1                 484                  \/     2            2         
- - - ------------------------------------------------------ + ---------------------------- + I*|- ------------------------------------------------------ + ---------------------------- + ----------------------------------| - ---------------------------------- + - - - ------------------------------------------------------ + ---------------------------- + I*|- ------------------------------------------------------ + ---------------------------- - ----------------------------------| + ---------------------------------- + - - - -------------------------------- - ------------------------------
  3                             3                                           3                   \                            3                                           3                                 3                 /                   3                      3                             3                                           3                   \                            3                                           3                                 3                 /                   3                      3          _________________________                 3               
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        /              __________                                  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       /  3611   3*I*\/ 48942255                                   
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  3*3 /   ---- + ----------------                                  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    \/     2            2
((−113sin⁡(atan⁡(3489422553611)3)3−13−484re⁡(1(−12−3i2)36112+348942255i23)3+11cos⁡(atan⁡(3489422553611)3)3+i(−484im⁡(1(−12−3i2)36112+348942255i23)3+11sin⁡(atan⁡(3489422553611)3)3+113cos⁡(atan⁡(3489422553611)3)3))+(−13+113sin⁡(atan⁡(3489422553611)3)3+11cos⁡(atan⁡(3489422553611)3)3−484re⁡(1(−12+3i2)36112+348942255i23)3+i(−113cos⁡(atan⁡(3489422553611)3)3+11sin⁡(atan⁡(3489422553611)3)3−484im⁡(1(−12+3i2)36112+348942255i23)3)))+(−13−36112+348942255i233−484336112+348942255i23)\left(\left(- \frac{11 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{1}{3} - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{11 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + i \left(- \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3}\right)\right) + \left(- \frac{1}{3} + \frac{11 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + i \left(- \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3}\right)\right)\right) + \left(- \frac{1}{3} - \frac{\sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}{3} - \frac{484}{3 \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right) 
=
                                              /                      1                       \         /                      1                       \                                                                     /        /                      1                       \                                                                    \     /        /                      1                       \                                                                    \
                                        484*re|----------------------------------------------|   484*re|----------------------------------------------|                                          /    /    __________\\     |  484*im|----------------------------------------------|         /    /    __________\\               /    /    __________\\|     |  484*im|----------------------------------------------|         /    /    __________\\               /    /    __________\\|
                                              |                     _________________________|         |                     _________________________|        _________________________         |    |3*\/ 48942255 ||     |        |                     _________________________|         |    |3*\/ 48942255 ||               |    |3*\/ 48942255 |||     |        |                     _________________________|         |    |3*\/ 48942255 ||               |    |3*\/ 48942255 |||
                                              |/          ___\     /              __________ |         |/          ___\     /              __________ |       /              __________          |atan|--------------||     |        |/          ___\     /              __________ |         |atan|--------------||               |atan|--------------|||     |        |/          ___\     /              __________ |         |atan|--------------||               |atan|--------------|||
                                              ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |         ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |      /  3611   3*I*\/ 48942255           |    \     3611     /|     |        ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |         |    \     3611     /|        ___    |    \     3611     /||     |        ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |         |    \     3611     /|        ___    |    \     3611     /||
                                              ||- - + -------|*3 /   ---- + ---------------- |         ||- - - -------|*3 /   ---- + ---------------- |   3 /   ---- + ----------------    22*cos|--------------------|     |        ||- - + -------|*3 /   ---- + ---------------- |   11*sin|--------------------|   11*\/ 3 *cos|--------------------||     |        ||- - - -------|*3 /   ---- + ---------------- |   11*sin|--------------------|   11*\/ 3 *cos|--------------------||
                   484                        \\  2      2   / \/     2            2         /         \\  2      2   / \/     2            2         /   \/     2            2                  \         3          /     |        \\  2      2   / \/     2            2         /         \         3          /               \         3          /|     |        \\  2      2   / \/     2            2         /         \         3          /               \         3          /|
-1 - -------------------------------- - ------------------------------------------------------ - ------------------------------------------------------ - ------------------------------ + ---------------------------- + I*|- ------------------------------------------------------ + ---------------------------- - ----------------------------------| + I*|- ------------------------------------------------------ + ---------------------------- + ----------------------------------|
            _________________________                             3                                                        3                                            3                               3                   \                            3                                           3                                 3                 /     \                            3                                           3                                 3                 /
           /              __________                                                                                                                                                                                                                                                                                                                                                                                                                                                         
          /  3611   3*I*\/ 48942255                                                                                                                                                                                                                                                                                                                                                                                                                                                          
     3*3 /   ---- + ----------------                                                                                                                                                                                                                                                                                                                                                                                                                                                         
       \/     2            2
−1−484re⁡(1(−12−3i2)36112+348942255i23)3−484re⁡(1(−12+3i2)36112+348942255i23)3+22cos⁡(atan⁡(3489422553611)3)3−36112+348942255i233+i(−113cos⁡(atan⁡(3489422553611)3)3+11sin⁡(atan⁡(3489422553611)3)3−484im⁡(1(−12+3i2)36112+348942255i23)3)+i(−484im⁡(1(−12−3i2)36112+348942255i23)3+11sin⁡(atan⁡(3489422553611)3)3+113cos⁡(atan⁡(3489422553611)3)3)−484336112+348942255i23-1 - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{22 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{\sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}{3} + i \left(- \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3}\right) + i \left(- \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3}\right) - \frac{484}{3 \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}} 
producto
/            /                      1                       \                                    /        /                      1                       \                                                                    \                                     \ /            /                      1                       \                                    /        /                      1                       \                                                                    \                                     \                                                                          
|      484*re|----------------------------------------------|         /    /    __________\\     |  484*im|----------------------------------------------|         /    /    __________\\               /    /    __________\\|               /    /    __________\\| |      484*re|----------------------------------------------|         /    /    __________\\     |  484*im|----------------------------------------------|         /    /    __________\\               /    /    __________\\|               /    /    __________\\|                                                                          
|            |                     _________________________|         |    |3*\/ 48942255 ||     |        |                     _________________________|         |    |3*\/ 48942255 ||               |    |3*\/ 48942255 |||               |    |3*\/ 48942255 ||| |            |                     _________________________|         |    |3*\/ 48942255 ||     |        |                     _________________________|         |    |3*\/ 48942255 ||               |    |3*\/ 48942255 |||               |    |3*\/ 48942255 ||| /                                              _________________________\
|            |/          ___\     /              __________ |         |atan|--------------||     |        |/          ___\     /              __________ |         |atan|--------------||               |atan|--------------|||               |atan|--------------||| |            |/          ___\     /              __________ |         |atan|--------------||     |        |/          ___\     /              __________ |         |atan|--------------||               |atan|--------------|||               |atan|--------------||| |                                             /              __________ |
|            ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |         |    \     3611     /|     |        ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |         |    \     3611     /|        ___    |    \     3611     /||        ___    |    \     3611     /|| |            ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |         |    \     3611     /|     |        ||  1   I*\/ 3 |    /  3611   3*I*\/ 48942255  |         |    \     3611     /|        ___    |    \     3611     /||        ___    |    \     3611     /|| |                                            /  3611   3*I*\/ 48942255  |
|            ||- - - -------|*3 /   ---- + ---------------- |   11*cos|--------------------|     |        ||- - - -------|*3 /   ---- + ---------------- |   11*sin|--------------------|   11*\/ 3 *cos|--------------------||   11*\/ 3 *sin|--------------------|| |            ||- - + -------|*3 /   ---- + ---------------- |   11*cos|--------------------|     |        ||- - + -------|*3 /   ---- + ---------------- |   11*sin|--------------------|   11*\/ 3 *cos|--------------------||   11*\/ 3 *sin|--------------------|| |                                         3 /   ---- + ---------------- |
|  1         \\  2      2   / \/     2            2         /         \         3          /     |        \\  2      2   / \/     2            2         /         \         3          /               \         3          /|               \         3          /| |  1         \\  2      2   / \/     2            2         /         \         3          /     |        \\  2      2   / \/     2            2         /         \         3          /               \         3          /|               \         3          /| |  1                 484                  \/     2            2         |
|- - - ------------------------------------------------------ + ---------------------------- + I*|- ------------------------------------------------------ + ---------------------------- + ----------------------------------| - ----------------------------------|*|- - - ------------------------------------------------------ + ---------------------------- + I*|- ------------------------------------------------------ + ---------------------------- - ----------------------------------| + ----------------------------------|*|- - - -------------------------------- - ------------------------------|
\  3                             3                                           3                   \                            3                                           3                                 3                 /                   3                 / \  3                             3                                           3                   \                            3                                           3                                 3                 /                   3                 / |  3          _________________________                 3               |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |            /              __________                                  |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |           /  3611   3*I*\/ 48942255                                   |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |      3*3 /   ---- + ----------------                                  |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \        \/     2            2                                          /
(−13+113sin⁡(atan⁡(3489422553611)3)3+11cos⁡(atan⁡(3489422553611)3)3−484re⁡(1(−12+3i2)36112+348942255i23)3+i(−113cos⁡(atan⁡(3489422553611)3)3+11sin⁡(atan⁡(3489422553611)3)3−484im⁡(1(−12+3i2)36112+348942255i23)3))(−113sin⁡(atan⁡(3489422553611)3)3−13−484re⁡(1(−12−3i2)36112+348942255i23)3+11cos⁡(atan⁡(3489422553611)3)3+i(−484im⁡(1(−12−3i2)36112+348942255i23)3+11sin⁡(atan⁡(3489422553611)3)3+113cos⁡(atan⁡(3489422553611)3)3))(−13−36112+348942255i233−484336112+348942255i23)\left(- \frac{1}{3} + \frac{11 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + i \left(- \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3}\right)\right) \left(- \frac{11 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} - \frac{1}{3} - \frac{484 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{11 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + i \left(- \frac{484 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right)}}{3} + \frac{11 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3} + \frac{11 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)}}{3}\right)\right) \left(- \frac{1}{3} - \frac{\sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}{3} - \frac{484}{3 \sqrt[3]{\frac{3611}{2} + \frac{3 \sqrt{48942255} i}{2}}}\right) 
=
                                                                                   /             /      /    __________\\         /    /    __________\\\
                                                                                   |             |      |3*\/ 48942255 ||         |    |3*\/ 48942255 |||
/               _________________________ /            _________________________\\ |             |2*atan|--------------||         |atan|--------------|||
|    3 ___   3 /              __________  |     2/3 3 /              __________ || |             |      \     3611     /|         |    \     3611     /||
\968*\/ 2  + \/  3611 + 3*I*\/ 48942255  *\2 + 2   *\/  3611 + 3*I*\/ 48942255  //*|483 - 968*cos|----------------------| + 44*cos|--------------------||
                                                                                   \             \          3           /         \         3          //
---------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                   _________________________                                                             
                                                                3 /              __________                                                              
                                                             54*\/  3611 + 3*I*\/ 48942255
(96823+(2+2233611+348942255i3)3611+348942255i3)(−968cos⁡(2atan⁡(3489422553611)3)+44cos⁡(atan⁡(3489422553611)3)+483)543611+348942255i3\frac{\left(968 \sqrt[3]{2} + \left(2 + 2^{\frac{2}{3}} \sqrt[3]{3611 + 3 \sqrt{48942255} i}\right) \sqrt[3]{3611 + 3 \sqrt{48942255} i}\right) \left(- 968 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)} + 44 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{48942255}}{3611} \right)}}{3} \right)} + 483\right)}{54 \sqrt[3]{3611 + 3 \sqrt{48942255} i}} 
(968*2^(1/3) + (3611 + 3*i*sqrt(48942255))^(1/3)*(2 + 2^(2/3)*(3611 + 3*i*sqrt(48942255))^(1/3)))*(483 - 968*cos(2*atan(3*sqrt(48942255)/3611)/3) + 44*cos(atan(3*sqrt(48942255)/3611)/3))/(54*(3611 + 3*i*sqrt(48942255))^(1/3))
Respuesta numérica [src] 
x1 = 11.9316179797821
x2 = 0.499215080312488
x3 = -13.4308330600946
x3 = -13.4308330600946
    © Sr Examen – Калькулятор