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La ecuación:
Ecuación 6x+1=-4x
Ecuación x+y-3=0
Ecuación x^2=-3
Ecuación 9-7(x+3)=5-6x
Expresar {x} en función de y en la ecuación:
-11*x+9*y=-20
5*x-14*y=-15
-10*x+15*y=10
-9*x-6*y=12
Expresiones idénticas
uno /(x- cuatro)^ dos - siete /x- cuatro + diez = cero
1 dividir por (x menos 4) al cuadrado menos 7 dividir por x menos 4 más 10 es igual a 0
uno dividir por (x menos cuatro) en el grado dos menos siete dividir por x menos cuatro más diez es igual a cero
1/(x-4)2-7/x-4+10=0
1/x-42-7/x-4+10=0
1/(x-4)²-7/x-4+10=0
1/(x-4) en el grado 2-7/x-4+10=0
1/x-4^2-7/x-4+10=0
1/(x-4)^2-7/x-4+10=O
1 dividir por (x-4)^2-7 dividir por x-4+10=0
Expresiones semejantes
1/(x-4)^2+7/x-4+10=0
1/(x-4)^2-7/x-4-10=0
1/(x-4)^2-7/x+4+10=0
1/(x+4)^2-7/x-4+10=0

1/(x-4)^2-7/x-4+10=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

   1       7             
-------- - - - 4 + 10 = 0
       2   x             
(x - 4)

\left(\left(\frac{1}{\left(x - 4\right)^{2}} - \frac{7}{x}\right) - 4\right) + 10 = 0

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

          ___________________                                    /                                            ___________________\             ___________________                                    /             ___________________                               \                                            ___________________
         /          ________                                     |                                           /          ________ |            /          ________                                     |            /          ________                                |                                           /          ________ 
        /  3199   \/ 259653                                      |                                   ___    /  3199   \/ 259653  |           /  3199   \/ 259653                                      |    ___    /  3199   \/ 259653                                 |                                          /  3199   \/ 259653  
     3 /   ---- + ----------                                     |                 ___             \/ 3 *3 /   ---- + ---------- |        3 /   ---- + ----------                                     |  \/ 3 *3 /   ---- + ----------                   ___          |                                       3 /   ---- + ---------- 
55   \/    108        24                    271                  |           271*\/ 3                    \/    108        24     |   55   \/    108        24                    271                  |        \/    108        24                 271*\/ 3           |   55               271                \/    108        24     
-- + ------------------------ + ---------------------------- + I*|- ---------------------------- + ------------------------------| + -- + ------------------------ + ---------------------------- + I*|- ------------------------------ + ----------------------------| + -- - ---------------------------- - ------------------------
18              6                        ___________________     |           ___________________                 6               |   18              6                        ___________________     |                6                           ___________________|   18            ___________________              3            
                                        /          ________      |          /          ________                                  |                                           /          ________      |                                           /          ________ |                /          ________                            
                                       /  3199   \/ 259653       |         /  3199   \/ 259653                                   |                                          /  3199   \/ 259653       |                                          /  3199   \/ 259653  |               /  3199   \/ 259653                             
                                216*3 /   ---- + ----------      |  216*3 /   ---- + ----------                                  |                                   216*3 /   ---- + ----------      |                                   216*3 /   ---- + ---------- |        108*3 /   ---- + ----------                            
                                    \/    108        24          \      \/    108        24                                      /                                       \/    108        24          \                                       \/    108        24     /            \/    108        24

\left(- \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{3} - \frac{271}{108 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{55}{18}\right) + \left(\left(\frac{271}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{55}{18} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}\right)\right) + \left(\frac{271}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{55}{18} + i \left(- \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6}\right)\right)\right)

       /                                            ___________________\     /             ___________________                               \
       |                                           /          ________ |     |            /          ________                                |
       |                                   ___    /  3199   \/ 259653  |     |    ___    /  3199   \/ 259653                                 |
       |                 ___             \/ 3 *3 /   ---- + ---------- |     |  \/ 3 *3 /   ---- + ----------                   ___          |
55     |           271*\/ 3                    \/    108        24     |     |        \/    108        24                 271*\/ 3           |
-- + I*|- ---------------------------- + ------------------------------| + I*|- ------------------------------ + ----------------------------|
6      |           ___________________                 6               |     |                6                           ___________________|
       |          /          ________                                  |     |                                           /          ________ |
       |         /  3199   \/ 259653                                   |     |                                          /  3199   \/ 259653  |
       |  216*3 /   ---- + ----------                                  |     |                                   216*3 /   ---- + ---------- |
       \      \/    108        24                                      /     \                                       \/    108        24     /

\frac{55}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}\right) + i \left(- \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6}\right)

producto

/          ___________________                                    /                                            ___________________\\ /          ___________________                                    /             ___________________                               \\ /                                         ___________________\
|         /          ________                                     |                                           /          ________ || |         /          ________                                     |            /          ________                                || |                                        /          ________ |
|        /  3199   \/ 259653                                      |                                   ___    /  3199   \/ 259653  || |        /  3199   \/ 259653                                      |    ___    /  3199   \/ 259653                                 || |                                       /  3199   \/ 259653  |
|     3 /   ---- + ----------                                     |                 ___             \/ 3 *3 /   ---- + ---------- || |     3 /   ---- + ----------                                     |  \/ 3 *3 /   ---- + ----------                   ___          || |                                    3 /   ---- + ---------- |
|55   \/    108        24                    271                  |           271*\/ 3                    \/    108        24     || |55   \/    108        24                    271                  |        \/    108        24                 271*\/ 3           || |55               271                \/    108        24     |
|-- + ------------------------ + ---------------------------- + I*|- ---------------------------- + ------------------------------||*|-- + ------------------------ + ---------------------------- + I*|- ------------------------------ + ----------------------------||*|-- - ---------------------------- - ------------------------|
|18              6                        ___________________     |           ___________________                 6               || |18              6                        ___________________     |                6                           ___________________|| |18            ___________________              3            |
|                                        /          ________      |          /          ________                                  || |                                        /          ________      |                                           /          ________ || |             /          ________                            |
|                                       /  3199   \/ 259653       |         /  3199   \/ 259653                                   || |                                       /  3199   \/ 259653       |                                          /  3199   \/ 259653  || |            /  3199   \/ 259653                             |
|                                216*3 /   ---- + ----------      |  216*3 /   ---- + ----------                                  || |                                216*3 /   ---- + ----------      |                                   216*3 /   ---- + ---------- || |     108*3 /   ---- + ----------                            |
\                                    \/    108        24          \      \/    108        24                                      // \                                    \/    108        24          \                                       \/    108        24     // \         \/    108        24                                /

\left(\frac{271}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{55}{18} + i \left(- \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6}\right)\right) \left(\frac{271}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{55}{18} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{3} - \frac{271}{108 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{55}{18}\right)

56/3

\frac{56}{3}

56/3

Respuesta rápida [src]

               ___________________                                    /                                            ___________________\
              /          ________                                     |                                           /          ________ |
             /  3199   \/ 259653                                      |                                   ___    /  3199   \/ 259653  |
          3 /   ---- + ----------                                     |                 ___             \/ 3 *3 /   ---- + ---------- |
     55   \/    108        24                    271                  |           271*\/ 3                    \/    108        24     |
x1 = -- + ------------------------ + ---------------------------- + I*|- ---------------------------- + ------------------------------|
     18              6                        ___________________     |           ___________________                 6               |
                                             /          ________      |          /          ________                                  |
                                            /  3199   \/ 259653       |         /  3199   \/ 259653                                   |
                                     216*3 /   ---- + ----------      |  216*3 /   ---- + ----------                                  |
                                         \/    108        24          \      \/    108        24                                      /

x_{1} = \frac{271}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{55}{18} + i \left(- \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6}\right)

               ___________________                                    /             ___________________                               \
              /          ________                                     |            /          ________                                |
             /  3199   \/ 259653                                      |    ___    /  3199   \/ 259653                                 |
          3 /   ---- + ----------                                     |  \/ 3 *3 /   ---- + ----------                   ___          |
     55   \/    108        24                    271                  |        \/    108        24                 271*\/ 3           |
x2 = -- + ------------------------ + ---------------------------- + I*|- ------------------------------ + ----------------------------|
     18              6                        ___________________     |                6                           ___________________|
                                             /          ________      |                                           /          ________ |
                                            /  3199   \/ 259653       |                                          /  3199   \/ 259653  |
                                     216*3 /   ---- + ----------      |                                   216*3 /   ---- + ---------- |
                                         \/    108        24          \                                       \/    108        24     /

x_{2} = \frac{271}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{55}{18} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{6} + \frac{271 \sqrt{3}}{216 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}\right)

                                              ___________________
                                             /          ________ 
                                            /  3199   \/ 259653  
                                         3 /   ---- + ---------- 
     55               271                \/    108        24     
x3 = -- - ---------------------------- - ------------------------
     18            ___________________              3            
                  /          ________                            
                 /  3199   \/ 259653                             
          108*3 /   ---- + ----------                            
              \/    108        24

x_{3} = - \frac{\sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}}{3} - \frac{271}{108 \sqrt[3]{\frac{\sqrt{259653}}{24} + \frac{3199}{108}}} + \frac{55}{18}

x3 = -(sqrt(259653)/24 + 3199/108)^(1/3)/3 - 271/(108*(sqrt(259653)/24 + 3199/108)^(1/3)) + 55/18

Respuesta numérica [src]

x1 = 4.01167510882973 + 0.482943621140577*i

x2 = 4.01167510882973 - 0.482943621140577*i

x3 = 1.1433164490072

x3 = 1.1433164490072

Gráfico

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1/(x-4)^2-7/x-4+10=0 la ecuación

Solución numérica:

Solución