Sr Examen

Otras calculadoras


1/(x-3)^2-8/x-3+15=0

1/(x-3)^2-8/x-3+15=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
   1       8             
-------- - - - 3 + 15 = 0
       2   x             
(x - 3)                  
$$\left(\left(\frac{1}{\left(x - 3\right)^{2}} - \frac{8}{x}\right) - 3\right) + 15 = 0$$
Gráfica
Respuesta rápida [src]
               _________________                                  /                                          _________________\
              /         _______                                   |                                         /         _______ |
             /  821   \/ 52413                                    |                                 ___    /  821   \/ 52413  |
          3 /   --- + ---------                                   |                ___            \/ 3 *3 /   --- + --------- |
     20   \/     54       24                  187                 |          187*\/ 3                   \/     54       24    |
x1 = -- + ---------------------- + -------------------------- + I*|- -------------------------- + ----------------------------|
     9              6                       _________________     |           _________________                6              |
                                           /         _______      |          /         _______                                |
                                          /  821   \/ 52413       |         /  821   \/ 52413                                 |
                                   216*3 /   --- + ---------      |  216*3 /   --- + ---------                                |
                                       \/     54       24         \      \/     54       24                                   /
$$x_{1} = \frac{187}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{20}{9} + i \left(- \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6}\right)$$
               _________________                                  /             _________________                             \
              /         _______                                   |            /         _______                              |
             /  821   \/ 52413                                    |    ___    /  821   \/ 52413                               |
          3 /   --- + ---------                                   |  \/ 3 *3 /   --- + ---------                  ___         |
     20   \/     54       24                  187                 |        \/     54       24               187*\/ 3          |
x2 = -- + ---------------------- + -------------------------- + I*|- ---------------------------- + --------------------------|
     9              6                       _________________     |               6                          _________________|
                                           /         _______      |                                         /         _______ |
                                          /  821   \/ 52413       |                                        /  821   \/ 52413  |
                                   216*3 /   --- + ---------      |                                 216*3 /   --- + --------- |
                                       \/     54       24         \                                     \/     54       24    /
$$x_{2} = \frac{187}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{20}{9} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}\right)$$
                                            _________________
                                           /         _______ 
                                          /  821   \/ 52413  
                                       3 /   --- + --------- 
     20              187               \/     54       24    
x3 = -- - -------------------------- - ----------------------
     9             _________________             3           
                  /         _______                          
                 /  821   \/ 52413                           
          108*3 /   --- + ---------                          
              \/     54       24                             
$$x_{3} = - \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{3} - \frac{187}{108 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{20}{9}$$
x3 = -(sqrt(52413)/24 + 821/54)^(1/3)/3 - 187/(108*(sqrt(52413)/24 + 821/54)^(1/3)) + 20/9
Suma y producto de raíces [src]
suma
          _________________                                  /                                          _________________\             _________________                                  /             _________________                             \                                          _________________
         /         _______                                   |                                         /         _______ |            /         _______                                   |            /         _______                              |                                         /         _______ 
        /  821   \/ 52413                                    |                                 ___    /  821   \/ 52413  |           /  821   \/ 52413                                    |    ___    /  821   \/ 52413                               |                                        /  821   \/ 52413  
     3 /   --- + ---------                                   |                ___            \/ 3 *3 /   --- + --------- |        3 /   --- + ---------                                   |  \/ 3 *3 /   --- + ---------                  ___         |                                     3 /   --- + --------- 
20   \/     54       24                  187                 |          187*\/ 3                   \/     54       24    |   20   \/     54       24                  187                 |        \/     54       24               187*\/ 3          |   20              187               \/     54       24    
-- + ---------------------- + -------------------------- + I*|- -------------------------- + ----------------------------| + -- + ---------------------- + -------------------------- + I*|- ---------------------------- + --------------------------| + -- - -------------------------- - ----------------------
9              6                       _________________     |           _________________                6              |   9              6                       _________________     |               6                          _________________|   9             _________________             3           
                                      /         _______      |          /         _______                                |                                         /         _______      |                                         /         _______ |                /         _______                          
                                     /  821   \/ 52413       |         /  821   \/ 52413                                 |                                        /  821   \/ 52413       |                                        /  821   \/ 52413  |               /  821   \/ 52413                           
                              216*3 /   --- + ---------      |  216*3 /   --- + ---------                                |                                 216*3 /   --- + ---------      |                                 216*3 /   --- + --------- |        108*3 /   --- + ---------                          
                                  \/     54       24         \      \/     54       24                                   /                                     \/     54       24         \                                     \/     54       24    /            \/     54       24                             
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{3} - \frac{187}{108 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{20}{9}\right) + \left(\left(\frac{187}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{20}{9} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}\right)\right) + \left(\frac{187}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{20}{9} + i \left(- \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6}\right)\right)\right)$$
=
       /                                          _________________\     /             _________________                             \
       |                                         /         _______ |     |            /         _______                              |
       |                                 ___    /  821   \/ 52413  |     |    ___    /  821   \/ 52413                               |
       |                ___            \/ 3 *3 /   --- + --------- |     |  \/ 3 *3 /   --- + ---------                  ___         |
20     |          187*\/ 3                   \/     54       24    |     |        \/     54       24               187*\/ 3          |
-- + I*|- -------------------------- + ----------------------------| + I*|- ---------------------------- + --------------------------|
3      |           _________________                6              |     |               6                          _________________|
       |          /         _______                                |     |                                         /         _______ |
       |         /  821   \/ 52413                                 |     |                                        /  821   \/ 52413  |
       |  216*3 /   --- + ---------                                |     |                                 216*3 /   --- + --------- |
       \      \/     54       24                                   /     \                                     \/     54       24    /
$$\frac{20}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}\right) + i \left(- \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6}\right)$$
producto
/          _________________                                  /                                          _________________\\ /          _________________                                  /             _________________                             \\ /                                       _________________\
|         /         _______                                   |                                         /         _______ || |         /         _______                                   |            /         _______                              || |                                      /         _______ |
|        /  821   \/ 52413                                    |                                 ___    /  821   \/ 52413  || |        /  821   \/ 52413                                    |    ___    /  821   \/ 52413                               || |                                     /  821   \/ 52413  |
|     3 /   --- + ---------                                   |                ___            \/ 3 *3 /   --- + --------- || |     3 /   --- + ---------                                   |  \/ 3 *3 /   --- + ---------                  ___         || |                                  3 /   --- + --------- |
|20   \/     54       24                  187                 |          187*\/ 3                   \/     54       24    || |20   \/     54       24                  187                 |        \/     54       24               187*\/ 3          || |20              187               \/     54       24    |
|-- + ---------------------- + -------------------------- + I*|- -------------------------- + ----------------------------||*|-- + ---------------------- + -------------------------- + I*|- ---------------------------- + --------------------------||*|-- - -------------------------- - ----------------------|
|9              6                       _________________     |           _________________                6              || |9              6                       _________________     |               6                          _________________|| |9             _________________             3           |
|                                      /         _______      |          /         _______                                || |                                      /         _______      |                                         /         _______ || |             /         _______                          |
|                                     /  821   \/ 52413       |         /  821   \/ 52413                                 || |                                     /  821   \/ 52413       |                                        /  821   \/ 52413  || |            /  821   \/ 52413                           |
|                              216*3 /   --- + ---------      |  216*3 /   --- + ---------                                || |                              216*3 /   --- + ---------      |                                 216*3 /   --- + --------- || |     108*3 /   --- + ---------                          |
\                                  \/     54       24         \      \/     54       24                                   // \                                  \/     54       24         \                                     \/     54       24    // \         \/     54       24                             /
$$\left(\frac{187}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{20}{9} + i \left(- \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6}\right)\right) \left(\frac{187}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{20}{9} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{6} + \frac{187 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}}{3} - \frac{187}{108 \sqrt[3]{\frac{\sqrt{52413}}{24} + \frac{821}{54}}} + \frac{20}{9}\right)$$
=
6
$$6$$
6
Respuesta numérica [src]
x1 = 3.00498310973485 + 0.326592007828122*i
x2 = 3.00498310973485 - 0.326592007828122*i
x3 = 0.65670044719696
x3 = 0.65670044719696
Gráfico
1/(x-3)^2-8/x-3+15=0 la ecuación