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- La ecuación:
-
Ecuación x^3-x^2-x-1=0
-
Ecuación 12-4(x-3)=39-9x
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Ecuación 0,2x+2,7=1,4-1,1x
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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
-
Expresiones idénticas
- ln|y|-y=ln|x|+x/ dos +C
- ln módulo de y| menos y es igual a ln|x| más x dividir por 2 más C
- ln módulo de y| menos y es igual a ln|x| más x dividir por dos más C
- ln|y|-y=ln|x|+x dividir por 2+C
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Expresiones semejantes
- ln|y|-y=ln|x|+x/2-C
- ln|y|+y=ln|x|+x/2+C
- ln|y|-y=ln|x|-x/2+C
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Expresiones con funciones
- ln
- ln(x/0,34)=22282,49539
- ln(x)=-2*x+14
- ln(2x^2+3)=0
- ln(2-cos(x))
- lnxy=-
- ln
- ln(x/0,34)=22282,49539
- ln(x)=-2*x+14
- ln(2x^2+3)=0
- ln(2-cos(x))
- lnxy=-
- Módulo |
- |3|x|-5|=-2x-2
- ||x|-4|=5
- |x-1|-2|x-2|+3|x-3|=4
- ||x-1|-2|=3x-4
- |x|=5
ln|y|-y=ln|x|+x/2+C la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
x
log(|y|) - y = log(|x|) + - + c
2
$$- y + \log{\left(\left|{y}\right| \right)} = c + \left(\frac{x}{2} + \log{\left(\left|{x}\right| \right)}\right)$$
Gráfica
Respuesta rápida
[src]
// / __________ \ / __________ \ \ // / __________ \ / __________ \ \
|| | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | |
y1 = I*im|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ <= 0| + re|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ <= 0|
|| | || |
\\ nan otherwise / \\ nan otherwise /
$$y_{1} = \operatorname{re}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
// / __________ \ / __________ \ \ // / __________ \ / __________ \ \
|| | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | |
y2 = I*im|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ > 0| + re|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ > 0|
|| | || |
\\ nan otherwise / \\ nan otherwise /
$$y_{2} = \operatorname{re}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
// / __________ \ / __________ \ \ // / __________ \ / __________ \ \
|| | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | |
y3 = I*im|<-W\\/ e *|x|/ for W\\/ e *|x|/ <= 0| + re|<-W\\/ e *|x|/ for W\\/ e *|x|/ <= 0|
|| | || |
\\ nan otherwise / \\ nan otherwise /
$$y_{3} = \operatorname{re}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
// / __________ \ / __________ \ \ // / __________ \ / __________ \ \
|| | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | |
y4 = I*im|<-W\\/ e *|x|/ for W\\/ e *|x|/ > 0| + re|<-W\\/ e *|x|/ for W\\/ e *|x|/ > 0|
|| | || |
\\ nan otherwise / \\ nan otherwise /
$$y_{4} = \operatorname{re}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
y4 = re(Piecewise((-LambertW(sqrt(exp(2*c + x))*|x|, LambertW(sqrt(exp(2*c + x))*|x|) > 0), (nan, True))) + i*im(Piecewise((-LambertW(sqrt(exp(2*c + x))*|x|), LambertW(sqrt(exp(2*c + x))*|x|) > 0), (nan, True))))
Suma y producto de raíces
[src]
suma
// / __________ \ / __________ \ \ // / __________ \ / __________ \ \ // / __________ \ / __________ \ \ // / __________ \ / __________ \ \ // / __________ \ / __________ \ \ // / __________ \ / __________ \ \ // / __________ \ / __________ \ \ // / __________ \ / __________ \ \
|| | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | |
I*im|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ <= 0| + re|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ <= 0| + I*im|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ > 0| + re|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ > 0| + I*im|<-W\\/ e *|x|/ for W\\/ e *|x|/ <= 0| + re|<-W\\/ e *|x|/ for W\\/ e *|x|/ <= 0| + I*im|<-W\\/ e *|x|/ for W\\/ e *|x|/ > 0| + re|<-W\\/ e *|x|/ for W\\/ e *|x|/ > 0|
|| | || | || | || | || | || | || | || |
\\ nan otherwise / \\ nan otherwise / \\ nan otherwise / \\ nan otherwise / \\ nan otherwise / \\ nan otherwise / \\ nan otherwise / \\ nan otherwise /
$$\left(\left(\left(\operatorname{re}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) + \left(\operatorname{re}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)\right) + \left(\operatorname{re}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)\right) + \left(\operatorname{re}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$
=
// / __________ \ / __________ \ \ // / __________ \ / __________ \ \ // / __________ \ / __________ \ \ // / __________ \ / __________ \ \ // / __________ \ / __________ \ \ // / __________ \ / __________ \ \ // / __________ \ / __________ \ \ // / __________ \ / __________ \ \
|| | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | |
I*im|<-W\\/ e *|x|/ for W\\/ e *|x|/ > 0| + I*im|<-W\\/ e *|x|/ for W\\/ e *|x|/ <= 0| + I*im|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ > 0| + I*im|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ <= 0| + re|<-W\\/ e *|x|/ for W\\/ e *|x|/ > 0| + re|<-W\\/ e *|x|/ for W\\/ e *|x|/ <= 0| + re|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ > 0| + re|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ <= 0|
|| | || | || | || | || | || | || | || |
\\ nan otherwise / \\ nan otherwise / \\ nan otherwise / \\ nan otherwise / \\ nan otherwise / \\ nan otherwise / \\ nan otherwise / \\ nan otherwise /
$$\operatorname{re}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
producto
/ // / __________ \ / __________ \ \ // / __________ \ / __________ \ \\ / // / __________ \ / __________ \ \ // / __________ \ / __________ \ \\ / // / __________ \ / __________ \ \ // / __________ \ / __________ \ \\ / // / __________ \ / __________ \ \ // / __________ \ / __________ \ \\ | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | || | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | || | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | || | || | / x + 2*c | | / x + 2*c | | || | / x + 2*c | | / x + 2*c | || |I*im|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ <= 0| + re|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ <= 0||*|I*im|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ > 0| + re|<-W\-\/ e *|x|/ for W\-\/ e *|x|/ > 0||*|I*im|<-W\\/ e *|x|/ for W\\/ e *|x|/ <= 0| + re|<-W\\/ e *|x|/ for W\\/ e *|x|/ <= 0||*|I*im|<-W\\/ e *|x|/ for W\\/ e *|x|/ > 0| + re|<-W\\/ e *|x|/ for W\\/ e *|x|/ > 0|| | || | || || | || | || || | || | || || | || | || || \ \\ nan otherwise / \\ nan otherwise // \ \\ nan otherwise / \\ nan otherwise // \ \\ nan otherwise / \\ nan otherwise // \ \\ nan otherwise / \\ nan otherwise //
$$\left(\operatorname{re}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(- \sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) & \text{for}\: W\left(\sqrt{e^{2 c + x}} \left|{x}\right|\right) > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$
=
nan
$$\text{NaN}$$
nan