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La ecuación:
Ecuación 4(x-3)=x+6
Ecuación (x-5)^2=(x+10)^2
Ecuación 3(x+3)=2x+5
Ecuación 2-3*(2*x+2)=5-4*x
Expresar {x} en función de y en la ecuación:
-11*x-15*y=14
12*x-13*y=-14
11*x-20*y=-10
-11*x+10*y=-9
Expresiones idénticas
-x^ tres + cuatro *x^ dos - cuatro *x+ ciento noventa y dos = cero
menos x al cubo más 4 multiplicar por x al cuadrado menos 4 multiplicar por x más 192 es igual a 0
menos x en el grado tres más cuatro multiplicar por x en el grado dos menos cuatro multiplicar por x más ciento noventa y dos es igual a cero
-x3+4*x2-4*x+192=0
-x³+4*x²-4*x+192=0
-x en el grado 3+4*x en el grado 2-4*x+192=0
-x^3+4x^2-4x+192=0
-x3+4x2-4x+192=0
-x^3+4*x^2-4*x+192=O
Expresiones semejantes
x^3+4*x^2-4*x+192=0
-x^3-4*x^2-4*x+192=0
-x^3+4*x^2-4*x-192=0
-x^3+4*x^2+4*x+192=0

-x^3+4x^2-4x+192=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

   3      2                
- x  + 4*x  - 4*x + 192 = 0

\left(- 4 x + \left(- x^{3} + 4 x^{2}\right)\right) + 192 = 0

Simplificar

Teorema de Cardano-Vieta

reescribamos la ecuación

\left(- 4 x + \left(- x^{3} + 4 x^{2}\right)\right) + 192 = 0

a x^{3} + b x^{2} + c x + d = 0

como ecuación cúbica reducida

x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0

x^{3} - 4 x^{2} + 4 x - 192 = 0

p x^{2} + q x + v + x^{3} = 0

donde

p = \frac{b}{a}

p = -4

q = \frac{c}{a}

q = 4

v = \frac{d}{a}

v = -192

Fórmulas de Cardano-Vieta

x_{1} + x_{2} + x_{3} = - p

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q

x_{1} x_{2} x_{3} = v

x_{1} + x_{2} + x_{3} = 4

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 4

x_{1} x_{2} x_{3} = -192

Suma y producto de raíces [src]

suma

         _________________                                /             _________________                           \            _________________                                /           _________________                           \              _________________                           
        /           _____                                 |            /           _____               ___          |           /           _____                                 |          /           _____               ___          |             /           _____                            
4      /  323   2*\/ 322                1                 |    ___    /  323   2*\/ 322              \/ 3           |   4      /  323   2*\/ 322                1                 |  ___    /  323   2*\/ 322              \/ 3           |   4        /  323   2*\/ 322                2            
- - 3 /   --- + ---------  - ------------------------ + I*|- \/ 3 *3 /   --- + ---------  + ------------------------| + - - 3 /   --- + ---------  - ------------------------ + I*|\/ 3 *3 /   --- + ---------  - ------------------------| + - + 2*3 /   --- + ---------  + ------------------------
3   \/     27       3               _________________     |        \/     27       3               _________________|   3   \/     27       3               _________________     |      \/     27       3               _________________|   3     \/     27       3               _________________
                                   /           _____      |                                       /           _____ |                                      /           _____      |                                     /           _____ |                                        /           _____ 
                                  /  323   2*\/ 322       |                                      /  323   2*\/ 322  |                                     /  323   2*\/ 322       |                                    /  323   2*\/ 322  |                                       /  323   2*\/ 322  
                             9*3 /   --- + ---------      |                                 9*3 /   --- + --------- |                                9*3 /   --- + ---------      |                               9*3 /   --- + --------- |                                  9*3 /   --- + --------- 
                               \/     27       3          \                                   \/     27       3     /                                  \/     27       3          \                                 \/     27       3     /                                    \/     27       3

\left(\frac{2}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}} + \frac{4}{3} + 2 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}\right) + \left(\left(- \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}} - \frac{1}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}} + \frac{4}{3} + i \left(- \sqrt{3} \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}} + \frac{\sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}}\right)\right) + \left(- \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}} - \frac{1}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}} + \frac{4}{3} + i \left(- \frac{\sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}} + \sqrt{3} \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}\right)\right)\right)

      /           _________________                           \     /             _________________                           \
      |          /           _____               ___          |     |            /           _____               ___          |
      |  ___    /  323   2*\/ 322              \/ 3           |     |    ___    /  323   2*\/ 322              \/ 3           |
4 + I*|\/ 3 *3 /   --- + ---------  - ------------------------| + I*|- \/ 3 *3 /   --- + ---------  + ------------------------|
      |      \/     27       3               _________________|     |        \/     27       3               _________________|
      |                                     /           _____ |     |                                       /           _____ |
      |                                    /  323   2*\/ 322  |     |                                      /  323   2*\/ 322  |
      |                               9*3 /   --- + --------- |     |                                 9*3 /   --- + --------- |
      \                                 \/     27       3     /     \                                   \/     27       3     /

4 + i \left(- \sqrt{3} \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}} + \frac{\sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}}\right) + i \left(- \frac{\sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}} + \sqrt{3} \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}\right)

producto

/         _________________                                /             _________________                           \\ /         _________________                                /           _________________                           \\ /           _________________                           \
|        /           _____                                 |            /           _____               ___          || |        /           _____                                 |          /           _____               ___          || |          /           _____                            |
|4      /  323   2*\/ 322                1                 |    ___    /  323   2*\/ 322              \/ 3           || |4      /  323   2*\/ 322                1                 |  ___    /  323   2*\/ 322              \/ 3           || |4        /  323   2*\/ 322                2            |
|- - 3 /   --- + ---------  - ------------------------ + I*|- \/ 3 *3 /   --- + ---------  + ------------------------||*|- - 3 /   --- + ---------  - ------------------------ + I*|\/ 3 *3 /   --- + ---------  - ------------------------||*|- + 2*3 /   --- + ---------  + ------------------------|
|3   \/     27       3               _________________     |        \/     27       3               _________________|| |3   \/     27       3               _________________     |      \/     27       3               _________________|| |3     \/     27       3               _________________|
|                                   /           _____      |                                       /           _____ || |                                   /           _____      |                                     /           _____ || |                                     /           _____ |
|                                  /  323   2*\/ 322       |                                      /  323   2*\/ 322  || |                                  /  323   2*\/ 322       |                                    /  323   2*\/ 322  || |                                    /  323   2*\/ 322  |
|                             9*3 /   --- + ---------      |                                 9*3 /   --- + --------- || |                             9*3 /   --- + ---------      |                               9*3 /   --- + --------- || |                               9*3 /   --- + --------- |
\                               \/     27       3          \                                   \/     27       3     // \                               \/     27       3          \                                 \/     27       3     // \                                 \/     27       3     /

\left(- \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}} - \frac{1}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}} + \frac{4}{3} + i \left(- \frac{\sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}} + \sqrt{3} \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}\right)\right) \left(- \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}} - \frac{1}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}} + \frac{4}{3} + i \left(- \sqrt{3} \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}} + \frac{\sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}}\right)\right) \left(\frac{2}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}} + \frac{4}{3} + 2 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}\right)

192

Respuesta rápida [src]

              _________________                                /             _________________                           \
             /           _____                                 |            /           _____               ___          |
     4      /  323   2*\/ 322                1                 |    ___    /  323   2*\/ 322              \/ 3           |
x1 = - - 3 /   --- + ---------  - ------------------------ + I*|- \/ 3 *3 /   --- + ---------  + ------------------------|
     3   \/     27       3               _________________     |        \/     27       3               _________________|
                                        /           _____      |                                       /           _____ |
                                       /  323   2*\/ 322       |                                      /  323   2*\/ 322  |
                                  9*3 /   --- + ---------      |                                 9*3 /   --- + --------- |
                                    \/     27       3          \                                   \/     27       3     /

x_{1} = - \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}} - \frac{1}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}} + \frac{4}{3} + i \left(- \sqrt{3} \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}} + \frac{\sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}}\right)

              _________________                                /           _________________                           \
             /           _____                                 |          /           _____               ___          |
     4      /  323   2*\/ 322                1                 |  ___    /  323   2*\/ 322              \/ 3           |
x2 = - - 3 /   --- + ---------  - ------------------------ + I*|\/ 3 *3 /   --- + ---------  - ------------------------|
     3   \/     27       3               _________________     |      \/     27       3               _________________|
                                        /           _____      |                                     /           _____ |
                                       /  323   2*\/ 322       |                                    /  323   2*\/ 322  |
                                  9*3 /   --- + ---------      |                               9*3 /   --- + --------- |
                                    \/     27       3          \                                 \/     27       3     /

x_{2} = - \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}} - \frac{1}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}} + \frac{4}{3} + i \left(- \frac{\sqrt{3}}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}} + \sqrt{3} \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}\right)

                _________________                           
               /           _____                            
     4        /  323   2*\/ 322                2            
x3 = - + 2*3 /   --- + ---------  + ------------------------
     3     \/     27       3               _________________
                                          /           _____ 
                                         /  323   2*\/ 322  
                                    9*3 /   --- + --------- 
                                      \/     27       3

x_{3} = \frac{2}{9 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}} + \frac{4}{3} + 2 \sqrt[3]{\frac{2 \sqrt{322}}{3} + \frac{323}{27}}

x3 = 2/(9*(2*sqrt(322)/3 + 323/27)^(1/3)) + 4/3 + 2*(2*sqrt(322)/3 + 323/27)^(1/3)

Respuesta numérica [src]

x1 = -1.58675266864455 - 4.92416220727021*i

x2 = -1.58675266864455 + 4.92416220727021*i

x3 = 7.1735053372891

x3 = 7.1735053372891

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Expresiones idénticas

Expresiones semejantes

-x^3+4*x^2-4*x+192=0 la ecuación

Solución numérica:

Solución

-x^3+4x^2-4x+192=0 la ecuación