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La ecuación:
Ecuación 3^x=27
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
Ecuación x(x^2+2x+1)=6(x+1)
Ecuación 4x+1=-3x+15
Expresar {x} en función de y en la ecuación:
-6*x-20*y=8
7*x-1*y=0
2*x-8*y=4
2*x-15*y=-1
Expresiones idénticas
(x- cuatro)/(x- tres)=x^ dos - seis *x+ dos / nueve
(x menos 4) dividir por (x menos 3) es igual a x al cuadrado menos 6 multiplicar por x más 2 dividir por 9
(x menos cuatro) dividir por (x menos tres) es igual a x en el grado dos menos seis multiplicar por x más dos dividir por nueve
(x-4)/(x-3)=x2-6*x+2/9
x-4/x-3=x2-6*x+2/9
(x-4)/(x-3)=x²-6*x+2/9
(x-4)/(x-3)=x en el grado 2-6*x+2/9
(x-4)/(x-3)=x^2-6x+2/9
(x-4)/(x-3)=x2-6x+2/9
x-4/x-3=x2-6x+2/9
x-4/x-3=x^2-6x+2/9
(x-4) dividir por (x-3)=x^2-6*x+2 dividir por 9
Expresiones semejantes
(x+4)/(x-3)=x^2-6*x+2/9
(x-3)/((x-1)(x-4))+((x-1)(x-4))/(x-3)=(5)/(2)
(x-4)/(x-3)=x^2-6*x-2/9
x-4/x-3+6/x^2=4/5
(x-4)/(x-3)=x^2+6*x+2/9
(x-4)/(x+3)=x^2-6*x+2/9

(x-4)/(x-3)=x^2-6*x+2/9 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

x - 4    2         2
----- = x  - 6*x + -
x - 3              9

\frac{x - 4}{x - 3} = \left(x^{2} - 6 x\right) + \frac{2}{9}

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

              /                    1                    \     /       /                    1                    \                                                                \                                                                
         88*re|-----------------------------------------|     |  88*im|-----------------------------------------|             /    /  _________\\             /    /  _________\\|             /    /  _________\\             /    /  _________\\
              |                     ____________________|     |       |                     ____________________|             |    |\/ 8118615 ||             |    |\/ 8118615 |||             |    |\/ 8118615 ||             |    |\/ 8118615 ||
              |/          ___\     /          _________ |     |       |/          ___\     /          _________ |             |atan|-----------||             |atan|-----------|||             |atan|-----------||             |atan|-----------||
              ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |     |       ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |     ____    |    \    243    /|     ____    |    \    243    /||     ____    |    \    243    /|     ____    |    \    243    /|
              ||- - - -------|*3 /   -- + ------------- |     |       ||- - - -------|*3 /   -- + ------------- |   \/ 22 *cos|-----------------|   \/ 66 *sin|-----------------||   \/ 22 *sin|-----------------|   \/ 66 *cos|-----------------|
              \\  2      2   / \/    2          18      /     |       \\  2      2   / \/    2          18      /             \        3        /             \        3        /|             \        3        /             \        3        /
x1 = 3 - ------------------------------------------------ + I*|- ------------------------------------------------ + ----------------------------- + -----------------------------| - ----------------------------- + -----------------------------
                                9                             \                         9                                         3                               9              /                 3                               9

x_{1} = - \frac{\sqrt{22} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{3} - \frac{88 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9} + \frac{\sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{9} + 3 + i \left(- \frac{88 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9} + \frac{\sqrt{66} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{9} + \frac{\sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{3}\right)

              /                    1                    \     /       /                    1                    \                                                                \                                                                
         88*re|-----------------------------------------|     |  88*im|-----------------------------------------|             /    /  _________\\             /    /  _________\\|             /    /  _________\\             /    /  _________\\
              |                     ____________________|     |       |                     ____________________|             |    |\/ 8118615 ||             |    |\/ 8118615 |||             |    |\/ 8118615 ||             |    |\/ 8118615 ||
              |/          ___\     /          _________ |     |       |/          ___\     /          _________ |             |atan|-----------||             |atan|-----------|||             |atan|-----------||             |atan|-----------||
              ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |     |       ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |     ____    |    \    243    /|     ____    |    \    243    /||     ____    |    \    243    /|     ____    |    \    243    /|
              ||- - + -------|*3 /   -- + ------------- |     |       ||- - + -------|*3 /   -- + ------------- |   \/ 22 *cos|-----------------|   \/ 66 *sin|-----------------||   \/ 22 *sin|-----------------|   \/ 66 *cos|-----------------|
              \\  2      2   / \/    2          18      /     |       \\  2      2   / \/    2          18      /             \        3        /             \        3        /|             \        3        /             \        3        /
x2 = 3 - ------------------------------------------------ + I*|- ------------------------------------------------ - ----------------------------- + -----------------------------| + ----------------------------- + -----------------------------
                                9                             \                         9                                         3                               9              /                 3                               9

x_{2} = \frac{\sqrt{22} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{3} + \frac{\sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{9} - \frac{88 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9} + 3 + i \left(- \frac{\sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{3} + \frac{\sqrt{66} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{9} - \frac{88 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9}\right)

                                            ____________________
                                           /          _________ 
                                          /  27   I*\/ 8118615  
                                       3 /   -- + ------------- 
                      88               \/    2          18      
x3 = 3 - --------------------------- - -------------------------
                ____________________               3            
               /          _________                             
              /  27   I*\/ 8118615                              
         9*3 /   -- + -------------                             
           \/    2          18

x_{3} = 3 - \frac{\sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}{3} - \frac{88}{9 \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}

x3 = 3 - (27/2 + sqrt(8118615)*i/18)^(1/3)/3 - 88/(9*(27/2 + sqrt(8118615)*i/18)^(1/3))

Suma y producto de raíces [src]

suma

         /                    1                    \     /       /                    1                    \                                                                \                                                                            /                    1                    \     /       /                    1                    \                                                                \                                                                                                                              
    88*re|-----------------------------------------|     |  88*im|-----------------------------------------|             /    /  _________\\             /    /  _________\\|             /    /  _________\\             /    /  _________\\       88*re|-----------------------------------------|     |  88*im|-----------------------------------------|             /    /  _________\\             /    /  _________\\|             /    /  _________\\             /    /  _________\\                                                              
         |                     ____________________|     |       |                     ____________________|             |    |\/ 8118615 ||             |    |\/ 8118615 |||             |    |\/ 8118615 ||             |    |\/ 8118615 ||            |                     ____________________|     |       |                     ____________________|             |    |\/ 8118615 ||             |    |\/ 8118615 |||             |    |\/ 8118615 ||             |    |\/ 8118615 ||                                          ____________________
         |/          ___\     /          _________ |     |       |/          ___\     /          _________ |             |atan|-----------||             |atan|-----------|||             |atan|-----------||             |atan|-----------||            |/          ___\     /          _________ |     |       |/          ___\     /          _________ |             |atan|-----------||             |atan|-----------|||             |atan|-----------||             |atan|-----------||                                         /          _________ 
         ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |     |       ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |     ____    |    \    243    /|     ____    |    \    243    /||     ____    |    \    243    /|     ____    |    \    243    /|            ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |     |       ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |     ____    |    \    243    /|     ____    |    \    243    /||     ____    |    \    243    /|     ____    |    \    243    /|                                        /  27   I*\/ 8118615  
         ||- - - -------|*3 /   -- + ------------- |     |       ||- - - -------|*3 /   -- + ------------- |   \/ 22 *cos|-----------------|   \/ 66 *sin|-----------------||   \/ 22 *sin|-----------------|   \/ 66 *cos|-----------------|            ||- - + -------|*3 /   -- + ------------- |     |       ||- - + -------|*3 /   -- + ------------- |   \/ 22 *cos|-----------------|   \/ 66 *sin|-----------------||   \/ 22 *sin|-----------------|   \/ 66 *cos|-----------------|                                     3 /   -- + ------------- 
         \\  2      2   / \/    2          18      /     |       \\  2      2   / \/    2          18      /             \        3        /             \        3        /|             \        3        /             \        3        /            \\  2      2   / \/    2          18      /     |       \\  2      2   / \/    2          18      /             \        3        /             \        3        /|             \        3        /             \        3        /                    88               \/    2          18      
3 - ------------------------------------------------ + I*|- ------------------------------------------------ + ----------------------------- + -----------------------------| - ----------------------------- + ----------------------------- + 3 - ------------------------------------------------ + I*|- ------------------------------------------------ - ----------------------------- + -----------------------------| + ----------------------------- + ----------------------------- + 3 - --------------------------- - -------------------------
                           9                             \                         9                                         3                               9              /                 3                               9                                            9                             \                         9                                         3                               9              /                 3                               9                            ____________________               3            
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          /          _________                             
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         /  27   I*\/ 8118615                              
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    9*3 /   -- + -------------                             
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      \/    2          18

\left(\left(- \frac{\sqrt{22} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{3} - \frac{88 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9} + \frac{\sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{9} + 3 + i \left(- \frac{88 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9} + \frac{\sqrt{66} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{9} + \frac{\sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{3}\right)\right) + \left(\frac{\sqrt{22} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{3} + \frac{\sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{9} - \frac{88 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9} + 3 + i \left(- \frac{\sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{3} + \frac{\sqrt{66} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{9} - \frac{88 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9}\right)\right)\right) + \left(3 - \frac{\sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}{3} - \frac{88}{9 \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)

                                       /                    1                    \        /                    1                    \                                 /       /                    1                    \                                                                \     /       /                    1                    \                                                                \                                  
                                  88*re|-----------------------------------------|   88*re|-----------------------------------------|                                 |  88*im|-----------------------------------------|             /    /  _________\\             /    /  _________\\|     |  88*im|-----------------------------------------|             /    /  _________\\             /    /  _________\\|               /    /  _________\\
                                       |                     ____________________|        |                     ____________________|        ____________________     |       |                     ____________________|             |    |\/ 8118615 ||             |    |\/ 8118615 |||     |       |                     ____________________|             |    |\/ 8118615 ||             |    |\/ 8118615 |||               |    |\/ 8118615 ||
                                       |/          ___\     /          _________ |        |/          ___\     /          _________ |       /          _________      |       |/          ___\     /          _________ |             |atan|-----------||             |atan|-----------|||     |       |/          ___\     /          _________ |             |atan|-----------||             |atan|-----------|||               |atan|-----------||
                                       ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |        ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |      /  27   I*\/ 8118615       |       ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |     ____    |    \    243    /|     ____    |    \    243    /||     |       ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |     ____    |    \    243    /|     ____    |    \    243    /||       ____    |    \    243    /|
                                       ||- - + -------|*3 /   -- + ------------- |        ||- - - -------|*3 /   -- + ------------- |   3 /   -- + -------------      |       ||- - + -------|*3 /   -- + ------------- |   \/ 22 *cos|-----------------|   \/ 66 *sin|-----------------||     |       ||- - - -------|*3 /   -- + ------------- |   \/ 22 *cos|-----------------|   \/ 66 *sin|-----------------||   2*\/ 66 *cos|-----------------|
                 88                    \\  2      2   / \/    2          18      /        \\  2      2   / \/    2          18      /   \/    2          18           |       \\  2      2   / \/    2          18      /             \        3        /             \        3        /|     |       \\  2      2   / \/    2          18      /             \        3        /             \        3        /|               \        3        /
9 - --------------------------- - ------------------------------------------------ - ------------------------------------------------ - ------------------------- + I*|- ------------------------------------------------ - ----------------------------- + -----------------------------| + I*|- ------------------------------------------------ + ----------------------------- + -----------------------------| + -------------------------------
           ____________________                          9                                                  9                                       3                 \                         9                                         3                               9              /     \                         9                                         3                               9              /                  9               
          /          _________                                                                                                                                                                                                                                                                                                                                                                                                                       
         /  27   I*\/ 8118615                                                                                                                                                                                                                                                                                                                                                                                                                        
    9*3 /   -- + -------------                                                                                                                                                                                                                                                                                                                                                                                                                       
      \/    2          18

- \frac{88 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9} - \frac{88 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9} + \frac{2 \sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{9} + 9 - \frac{\sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}{3} + i \left(- \frac{88 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9} + \frac{\sqrt{66} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{9} + \frac{\sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{3}\right) + i \left(- \frac{\sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{3} + \frac{\sqrt{66} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{9} - \frac{88 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9}\right) - \frac{88}{9 \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}

producto

/         /                    1                    \     /       /                    1                    \                                                                \                                                                \ /         /                    1                    \     /       /                    1                    \                                                                \                                                                \                                                              
|    88*re|-----------------------------------------|     |  88*im|-----------------------------------------|             /    /  _________\\             /    /  _________\\|             /    /  _________\\             /    /  _________\\| |    88*re|-----------------------------------------|     |  88*im|-----------------------------------------|             /    /  _________\\             /    /  _________\\|             /    /  _________\\             /    /  _________\\|                                                              
|         |                     ____________________|     |       |                     ____________________|             |    |\/ 8118615 ||             |    |\/ 8118615 |||             |    |\/ 8118615 ||             |    |\/ 8118615 ||| |         |                     ____________________|     |       |                     ____________________|             |    |\/ 8118615 ||             |    |\/ 8118615 |||             |    |\/ 8118615 ||             |    |\/ 8118615 ||| /                                       ____________________\
|         |/          ___\     /          _________ |     |       |/          ___\     /          _________ |             |atan|-----------||             |atan|-----------|||             |atan|-----------||             |atan|-----------||| |         |/          ___\     /          _________ |     |       |/          ___\     /          _________ |             |atan|-----------||             |atan|-----------|||             |atan|-----------||             |atan|-----------||| |                                      /          _________ |
|         ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |     |       ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |     ____    |    \    243    /|     ____    |    \    243    /||     ____    |    \    243    /|     ____    |    \    243    /|| |         ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |     |       ||  1   I*\/ 3 |    /  27   I*\/ 8118615  |     ____    |    \    243    /|     ____    |    \    243    /||     ____    |    \    243    /|     ____    |    \    243    /|| |                                     /  27   I*\/ 8118615  |
|         ||- - - -------|*3 /   -- + ------------- |     |       ||- - - -------|*3 /   -- + ------------- |   \/ 22 *cos|-----------------|   \/ 66 *sin|-----------------||   \/ 22 *sin|-----------------|   \/ 66 *cos|-----------------|| |         ||- - + -------|*3 /   -- + ------------- |     |       ||- - + -------|*3 /   -- + ------------- |   \/ 22 *cos|-----------------|   \/ 66 *sin|-----------------||   \/ 22 *sin|-----------------|   \/ 66 *cos|-----------------|| |                                  3 /   -- + ------------- |
|         \\  2      2   / \/    2          18      /     |       \\  2      2   / \/    2          18      /             \        3        /             \        3        /|             \        3        /             \        3        /| |         \\  2      2   / \/    2          18      /     |       \\  2      2   / \/    2          18      /             \        3        /             \        3        /|             \        3        /             \        3        /| |                 88               \/    2          18      |
|3 - ------------------------------------------------ + I*|- ------------------------------------------------ + ----------------------------- + -----------------------------| - ----------------------------- + -----------------------------|*|3 - ------------------------------------------------ + I*|- ------------------------------------------------ - ----------------------------- + -----------------------------| + ----------------------------- + -----------------------------|*|3 - --------------------------- - -------------------------|
\                           9                             \                         9                                         3                               9              /                 3                               9              / \                           9                             \                         9                                         3                               9              /                 3                               9              / |           ____________________               3            |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |          /          _________                             |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |         /  27   I*\/ 8118615                              |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |    9*3 /   -- + -------------                             |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                \      \/    2          18                                  /

\left(- \frac{\sqrt{22} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{3} - \frac{88 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9} + \frac{\sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{9} + 3 + i \left(- \frac{88 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9} + \frac{\sqrt{66} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{9} + \frac{\sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{3}\right)\right) \left(\frac{\sqrt{22} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{3} + \frac{\sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{9} - \frac{88 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9} + 3 + i \left(- \frac{\sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{3} + \frac{\sqrt{66} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}}{9} - \frac{88 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)}}{9}\right)\right) \left(3 - \frac{\sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}{3} - \frac{88}{9 \sqrt[3]{\frac{27}{2} + \frac{\sqrt{8118615} i}{18}}}\right)

                                                                             /             /      /  _________\\                 /    /  _________\\\ 
                                                                             |             |      |\/ 8118615 ||                 |    |\/ 8118615 ||| 
 /                _____________________ /        _________________________\\ |             |2*atan|-----------||                 |atan|-----------||| 
 |    3 ____   3 /           _________  |     3 /               _________ || |             |      \    243    /|         ____    |    \    243    /|| 
-\176*\/ 18  - \/  243 + I*\/ 8118615  *\54 - \/  2916 + 12*I*\/ 8118615  //*|465 + 528*cos|-------------------| + 108*\/ 66 *cos|-----------------|| 
                                                                             \             \         3         /                 \        3        // 
------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                    _____________________                                                             
                                                                 3 /           _________                                                              
                                                            1458*\/  243 + I*\/ 8118615

- \frac{\left(176 \sqrt[3]{18} - \left(54 - \sqrt[3]{2916 + 12 \sqrt{8118615} i}\right) \sqrt[3]{243 + \sqrt{8118615} i}\right) \left(528 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)} + 465 + 108 \sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{8118615}}{243} \right)}}{3} \right)}\right)}{1458 \sqrt[3]{243 + \sqrt{8118615} i}}

-(176*18^(1/3) - (243 + i*sqrt(8118615))^(1/3)*(54 - (2916 + 12*i*sqrt(8118615))^(1/3)))*(465 + 528*cos(2*atan(sqrt(8118615)/243)/3) + 108*sqrt(66)*cos(atan(sqrt(8118615)/243)/3))/(1458*(243 + i*sqrt(8118615))^(1/3))

Respuesta numérica [src]

x1 = 3.10238248543886 + 0.e-22*i

x2 = 6.07449526551909 - 0.e-22*i

x3 = -0.17687775095795 + 0.e-22*i

x3 = -0.17687775095795 + 0.e-22*i

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(x-4)/(x-3)=x^2-6*x+2/9 la ecuación

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