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- La ecuación:
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Ecuación x^4+2*x^2-8=0
-
Ecuación x*(x^2+8*x+16)=5*(x+4)
-
Ecuación -25-x=-17
-
Ecuación x^2+3x=4
- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- -14*x+10*y=19
- -9*x+1*y=3
- -17*x+1*y=-11
-
Expresiones idénticas
- ln(|x|)/ dos =-ln(|p- uno |)+C
- ln( módulo de x|) dividir por 2 es igual a menos ln(|p menos 1|) más C
- ln( módulo de x|) dividir por dos es igual a menos ln(|p menos uno |) más C
- ln|x|/2=-ln|p-1|+C
- ln(|x|) dividir por 2=-ln(|p-1|)+C
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Expresiones semejantes
- ln(|x|)/2=-ln(|p+1|)+C
- ln(|x|)/2=+ln(|p-1|)+C
- ln(|x|)/2=-ln(|p-1|)-C
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Expresiones con funciones
- ln
- ln(abs((1-x)/(1+x)))=0
- ln(x)=-1
- ln(-x+1)
- ln(x^2+1)*1/2=0
- ln*x+(x+1)^3=0
- ln
- ln(abs((1-x)/(1+x)))=0
- ln(x)=-1
- ln(-x+1)
- ln(x^2+1)*1/2=0
- ln*x+(x+1)^3=0
- Módulo |
- |x+2|+|x-3|=7
- ||3x-1|-5|=2x-3
- |x|=1
- |x|=-4
- |x|=-1
ln(|x|)/2=-ln(|p-1|)+C la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
log(|x|) -------- = -log(|p - 1|) + c 2
$$\frac{\log{\left(\left|{x}\right| \right)}}{2} = c - \log{\left(\left|{p - 1}\right| \right)}$$
Gráfica
Suma y producto de raíces
[src]
suma
// 2*c 2*c \ // 2*c 2*c \ // 2*c 2*c \ // 2*c 2*c \
|| e e | || e e | || -e e | || -e e |
||--------- for ----------- >= 0| ||--------- for ----------- >= 0| ||----------- for ----------- > 0| ||----------- for ----------- > 0|
I*im|< 2 | 2| | + re|< 2 | 2| | + I*im|<| 2| | 2| | + re|<| 2| | 2| |
|||-1 + p| |(-1 + p) | | |||-1 + p| |(-1 + p) | | |||(-1 + p) | |(-1 + p) | | |||(-1 + p) | |(-1 + p) | |
|| | || | || | || |
\\ nan otherwise / \\ nan otherwise / \\ nan otherwise / \\ nan otherwise /
$$\left(\operatorname{re}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) + \left(\operatorname{re}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$
=
// 2*c 2*c \ // 2*c 2*c \ // 2*c 2*c \ // 2*c 2*c \
|| e e | || -e e | || e e | || -e e |
||--------- for ----------- >= 0| ||----------- for ----------- > 0| ||--------- for ----------- >= 0| ||----------- for ----------- > 0|
I*im|< 2 | 2| | + I*im|<| 2| | 2| | + re|< 2 | 2| | + re|<| 2| | 2| |
|||-1 + p| |(-1 + p) | | |||(-1 + p) | |(-1 + p) | | |||-1 + p| |(-1 + p) | | |||(-1 + p) | |(-1 + p) | |
|| | || | || | || |
\\ nan otherwise / \\ nan otherwise / \\ nan otherwise / \\ nan otherwise /
$$\operatorname{re}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
producto
/ // 2*c 2*c \ // 2*c 2*c \\ / // 2*c 2*c \ // 2*c 2*c \\ | || e e | || e e || | || -e e | || -e e || | ||--------- for ----------- >= 0| ||--------- for ----------- >= 0|| | ||----------- for ----------- > 0| ||----------- for ----------- > 0|| |I*im|< 2 | 2| | + re|< 2 | 2| ||*|I*im|<| 2| | 2| | + re|<| 2| | 2| || | |||-1 + p| |(-1 + p) | | |||-1 + p| |(-1 + p) | || | |||(-1 + p) | |(-1 + p) | | |||(-1 + p) | |(-1 + p) | || | || | || || | || | || || \ \\ nan otherwise / \\ nan otherwise // \ \\ nan otherwise / \\ nan otherwise //
$$\left(\operatorname{re}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$
=
/ 4*re(c) + 4*I*im(c) / 2*c 2*c \ |-e | e e | |---------------------- for And|----------- >= 0, ----------- > 0| | 2 || 2| | 2| | < | 2| \|(-1 + p) | |(-1 + p) | / | |(-1 + p) | | | nan otherwise \
$$\begin{cases} - \frac{e^{4 \operatorname{re}{\left(c\right)} + 4 i \operatorname{im}{\left(c\right)}}}{\left|{\left(p - 1\right)^{2}}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \wedge \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}$$
Piecewise((-exp(4*re(c) + 4*i*im(c))/Abs((-1 + p)^2)^2, (exp(2*c)/Abs((-1 + p)^2) >= 0)∧(exp(2*c)/Abs((-1 + p)^2) > 0)), (nan, True))
Respuesta rápida
[src]
// 2*c 2*c \ // 2*c 2*c \
|| e e | || e e |
||--------- for ----------- >= 0| ||--------- for ----------- >= 0|
x1 = I*im|< 2 | 2| | + re|< 2 | 2| |
|||-1 + p| |(-1 + p) | | |||-1 + p| |(-1 + p) | |
|| | || |
\\ nan otherwise / \\ nan otherwise /
$$x_{1} = \operatorname{re}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{e^{2 c}}{\left|{p - 1}\right|^{2}} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
// 2*c 2*c \ // 2*c 2*c \
|| -e e | || -e e |
||----------- for ----------- > 0| ||----------- for ----------- > 0|
x2 = I*im|<| 2| | 2| | + re|<| 2| | 2| |
|||(-1 + p) | |(-1 + p) | | |||(-1 + p) | |(-1 + p) | |
|| | || |
\\ nan otherwise / \\ nan otherwise /
$$x_{2} = \operatorname{re}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} & \text{for}\: \frac{e^{2 c}}{\left|{\left(p - 1\right)^{2}}\right|} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
x2 = re(Piecewise((-exp(2*c)/Abs((p - 1)^2, exp(2*c)/Abs((p - 1)^2) > 0), (nan, True))) + i*im(Piecewise((-exp(2*c)/Abs((p - 1)^2), exp(2*c)/Abs((p - 1)^2) > 0), (nan, True))))