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La ecuación:
Ecuación x^3-x^2-x-1=0
Ecuación 12-4(x-3)=39-9x
Ecuación 0,2x+2,7=1,4-1,1x
Ecuación x^2=2x+8
Expresar {x} en función de y en la ecuación:
-11*x-14*y=-3
-9*x-1*y=6
-2*x+2*y=4
-11*x-3*y=14
Integral de d{x}:
ax
Derivada de:
ax
Suma de la serie:
ax
Expresiones idénticas
ax=4a+ catorce ∣x∣+2x−x2
ax es igual a 4a más 14∣x∣ más 2x−x2
ax es igual a 4a más cotangente de angente de orce ∣x∣ más 2x−x2
Expresiones semejantes
ax=4a-14∣x∣+2x−x2
ax=4a+14∣x∣-2x−x2
a*x+b=c
a*x+b*y+c=0
Expresiones con funciones
ax
ax+b=c
ax+√(3-2x-x^2)=4a+2
ax+lny=y+b
ax^3-6x^2-3ax=2
ax^2=c

ax=4a+14∣x∣+2x−x2 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

a*x = 4*a + 14*|x| + 2*x - x2

$$a x = - x_{2} + \left(2 x + \left(4 a + 14 \left|{x}\right|\right)\right)$$

Simplificar

Solución detallada

Para cada expresión dentro del módulo en la ecuación
admitimos los casos cuando la expresión correspondiente es ">= 0" o "< 0",
resolvemos las ecuaciones obtenidas.

1.
$$x \geq 0$$
o
$$0 \leq x \wedge x < \infty$$
obtenemos la ecuación
$$a x - 4 a - 14 x - 2 x + x_{2} = 0$$
simplificamos, obtenemos
$$a x - 4 a - 16 x + x_{2} = 0$$
la resolución en este intervalo:
$$x_{1} = \frac{4 a - x_{2}}{a - 16}$$

2.
$$x < 0$$
o
$$-\infty < x \wedge x < 0$$
obtenemos la ecuación
$$a x - 4 a - 2 x - 14 \left(- x\right) + x_{2} = 0$$
simplificamos, obtenemos
$$a x - 4 a + 12 x + x_{2} = 0$$
la resolución en este intervalo:
$$x_{2} = \frac{4 a - x_{2}}{a + 12}$$

Entonces la respuesta definitiva es:
$$x_{1} = \frac{4 a - x_{2}}{a - 16}$$
$$x_{2} = \frac{4 a - x_{2}}{a + 12}$$

Gráfica

Respuesta rápida [src]

         //-x2 + 4*a      -x2 + 4*a     \     //-x2 + 4*a      -x2 + 4*a     \
         ||---------  for --------- >= 0|     ||---------  for --------- >= 0|
x1 = I*im|< -16 + a        -16 + a      | + re|< -16 + a        -16 + a      |
         ||                             |     ||                             |
         \\   nan         otherwise     /     \\   nan         otherwise     /

$$x_{1} = \operatorname{re}{\left(\begin{cases} \frac{4 a - x_{2}}{a - 16} & \text{for}\: \frac{4 a - x_{2}}{a - 16} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{4 a - x_{2}}{a - 16} & \text{for}\: \frac{4 a - x_{2}}{a - 16} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$

         //-x2 + 4*a      -x2 + 4*a    \     //-x2 + 4*a      -x2 + 4*a    \
         ||---------  for --------- < 0|     ||---------  for --------- < 0|
x2 = I*im|<  12 + a         12 + a     | + re|<  12 + a         12 + a     |
         ||                            |     ||                            |
         \\   nan         otherwise    /     \\   nan         otherwise    /

$$x_{2} = \operatorname{re}{\left(\begin{cases} \frac{4 a - x_{2}}{a + 12} & \text{for}\: \frac{4 a - x_{2}}{a + 12} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{4 a - x_{2}}{a + 12} & \text{for}\: \frac{4 a - x_{2}}{a + 12} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$

x2 = re(Piecewise(((4*a - x2)/(a + 12, (4*a - x2)/(a + 12) < 0), (nan, True))) + i*im(Piecewise(((4*a - x2)/(a + 12), (4*a - x2)/(a + 12) < 0), (nan, True))))

Suma y producto de raíces [src]

suma

    //-x2 + 4*a      -x2 + 4*a     \     //-x2 + 4*a      -x2 + 4*a     \       //-x2 + 4*a      -x2 + 4*a    \     //-x2 + 4*a      -x2 + 4*a    \
    ||---------  for --------- >= 0|     ||---------  for --------- >= 0|       ||---------  for --------- < 0|     ||---------  for --------- < 0|
I*im|< -16 + a        -16 + a      | + re|< -16 + a        -16 + a      | + I*im|<  12 + a         12 + a     | + re|<  12 + a         12 + a     |
    ||                             |     ||                             |       ||                            |     ||                            |
    \\   nan         otherwise     /     \\   nan         otherwise     /       \\   nan         otherwise    /     \\   nan         otherwise    /

$$\left(\operatorname{re}{\left(\begin{cases} \frac{4 a - x_{2}}{a - 16} & \text{for}\: \frac{4 a - x_{2}}{a - 16} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{4 a - x_{2}}{a - 16} & \text{for}\: \frac{4 a - x_{2}}{a - 16} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) + \left(\operatorname{re}{\left(\begin{cases} \frac{4 a - x_{2}}{a + 12} & \text{for}\: \frac{4 a - x_{2}}{a + 12} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{4 a - x_{2}}{a + 12} & \text{for}\: \frac{4 a - x_{2}}{a + 12} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$

    //-x2 + 4*a      -x2 + 4*a     \       //-x2 + 4*a      -x2 + 4*a    \     //-x2 + 4*a      -x2 + 4*a     \     //-x2 + 4*a      -x2 + 4*a    \
    ||---------  for --------- >= 0|       ||---------  for --------- < 0|     ||---------  for --------- >= 0|     ||---------  for --------- < 0|
I*im|< -16 + a        -16 + a      | + I*im|<  12 + a         12 + a     | + re|< -16 + a        -16 + a      | + re|<  12 + a         12 + a     |
    ||                             |       ||                            |     ||                             |     ||                            |
    \\   nan         otherwise     /       \\   nan         otherwise    /     \\   nan         otherwise     /     \\   nan         otherwise    /

$$\operatorname{re}{\left(\begin{cases} \frac{4 a - x_{2}}{a - 16} & \text{for}\: \frac{4 a - x_{2}}{a - 16} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} \frac{4 a - x_{2}}{a + 12} & \text{for}\: \frac{4 a - x_{2}}{a + 12} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{4 a - x_{2}}{a - 16} & \text{for}\: \frac{4 a - x_{2}}{a - 16} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{4 a - x_{2}}{a + 12} & \text{for}\: \frac{4 a - x_{2}}{a + 12} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$

producto

/    //-x2 + 4*a      -x2 + 4*a     \     //-x2 + 4*a      -x2 + 4*a     \\ /    //-x2 + 4*a      -x2 + 4*a    \     //-x2 + 4*a      -x2 + 4*a    \\
|    ||---------  for --------- >= 0|     ||---------  for --------- >= 0|| |    ||---------  for --------- < 0|     ||---------  for --------- < 0||
|I*im|< -16 + a        -16 + a      | + re|< -16 + a        -16 + a      ||*|I*im|<  12 + a         12 + a     | + re|<  12 + a         12 + a     ||
|    ||                             |     ||                             || |    ||                            |     ||                            ||
\    \\   nan         otherwise     /     \\   nan         otherwise     // \    \\   nan         otherwise    /     \\   nan         otherwise    //

$$\left(\operatorname{re}{\left(\begin{cases} \frac{4 a - x_{2}}{a - 16} & \text{for}\: \frac{4 a - x_{2}}{a - 16} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{4 a - x_{2}}{a - 16} & \text{for}\: \frac{4 a - x_{2}}{a - 16} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} \frac{4 a - x_{2}}{a + 12} & \text{for}\: \frac{4 a - x_{2}}{a + 12} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{4 a - x_{2}}{a + 12} & \text{for}\: \frac{4 a - x_{2}}{a + 12} < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$

/(I*((-16 + re(a))*(-im(x2) + 4*im(a)) - (-re(x2) + 4*re(a))*im(a)) + (-16 + re(a))*(-re(x2) + 4*re(a)) + (-im(x2) + 4*im(a))*im(a))*(I*((12 + re(a))*(-im(x2) + 4*im(a)) - (-re(x2) + 4*re(a))*im(a)) + (12 + re(a))*(-re(x2) + 4*re(a)) + (-im(x2) + 4*im(a))*im(a))         /-x2 + 4*a       -x2 + 4*a    \
|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------  for And|--------- >= 0, --------- < 0|
|                                                                                                          /             2     2   \ /            2     2   \                                                                                                                  \ -16 + a          12 + a     /
<                                                                                                          \(-16 + re(a))  + im (a)/*\(12 + re(a))  + im (a)/                                                                                                                                                 
|                                                                                                                                                                                                                                                                                                             
|                                                                                                                                 nan                                                                                                                                                 otherwise               
\

$$\begin{cases} \frac{\left(i \left(\left(\operatorname{re}{\left(a\right)} - 16\right) \left(4 \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(x_{2}\right)}\right) - \left(4 \operatorname{re}{\left(a\right)} - \operatorname{re}{\left(x_{2}\right)}\right) \operatorname{im}{\left(a\right)}\right) + \left(\operatorname{re}{\left(a\right)} - 16\right) \left(4 \operatorname{re}{\left(a\right)} - \operatorname{re}{\left(x_{2}\right)}\right) + \left(4 \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(x_{2}\right)}\right) \operatorname{im}{\left(a\right)}\right) \left(i \left(\left(\operatorname{re}{\left(a\right)} + 12\right) \left(4 \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(x_{2}\right)}\right) - \left(4 \operatorname{re}{\left(a\right)} - \operatorname{re}{\left(x_{2}\right)}\right) \operatorname{im}{\left(a\right)}\right) + \left(\operatorname{re}{\left(a\right)} + 12\right) \left(4 \operatorname{re}{\left(a\right)} - \operatorname{re}{\left(x_{2}\right)}\right) + \left(4 \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(x_{2}\right)}\right) \operatorname{im}{\left(a\right)}\right)}{\left(\left(\operatorname{re}{\left(a\right)} - 16\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\left(\operatorname{re}{\left(a\right)} + 12\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} & \text{for}\: \frac{4 a - x_{2}}{a - 16} \geq 0 \wedge \frac{4 a - x_{2}}{a + 12} < 0 \\\text{NaN} & \text{otherwise} \end{cases}$$

Piecewise(((i*((-16 + re(a))*(-im(x2) + 4*im(a)) - (-re(x2) + 4*re(a))*im(a)) + (-16 + re(a))*(-re(x2) + 4*re(a)) + (-im(x2) + 4*im(a))*im(a))*(i*((12 + re(a))*(-im(x2) + 4*im(a)) - (-re(x2) + 4*re(a))*im(a)) + (12 + re(a))*(-re(x2) + 4*re(a)) + (-im(x2) + 4*im(a))*im(a))/(((-16 + re(a))^2 + im(a)^2)*((12 + re(a))^2 + im(a)^2)), ((-x2 + 4*a)/(-16 + a) >= 0)∧((-x2 + 4*a)/(12 + a) < 0)), (nan, True))

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Expresiones con funciones

ax=4a+14∣x∣+2x−x2 la ecuación

Solución numérica:

Solución