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- La ecuación:
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Ecuación x^4+2*x^2-8=0
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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
- Gráfico de la función y =:
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x.diff(x)
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Expresiones idénticas
- x.diff(x)=(dos *sin(t))*x+(log(t))*y
- x.diff(x) es igual a (2 multiplicar por seno de (t)) multiplicar por x más ( logaritmo de (t)) multiplicar por y
- x.diff(x) es igual a (dos multiplicar por seno de (t)) multiplicar por x más ( logaritmo de (t)) multiplicar por y
- x.diff(x)=(2sin(t))x+(log(t))y
- x.diffx=2sintx+logty
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Expresiones semejantes
- x.diff(x)=(2*sin(t))*x-(log(t))*y
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Expresiones con funciones
- Seno sin
- sin(x)=1,5
- sin(x-1)=0
- sin2x=1
- sin(3*x)=-1/2
- sin(3*x)=-1
- Logaritmo log
- log(x)=x
- log(2*y+1)/2=c+log(sin(x))
- log(2*x)=0
- log3x=-1
- log1/2(2x-6)=-2
x.diff(x)=(2*sin(t))*x+(log(t))*y la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/x for 0 = 1 | <1 for 1 = 1 = 2*sin(t)*x + log(t)*y | \0 otherwise
$$\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} = x 2 \sin{\left(t \right)} + y \log{\left(t \right)}$$
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} = 2 x \sin{\left(t \right)} + y \log{\left(t \right)}$$
Коэффициент при y равен
$$- \log{\left(t \right)}$$
entonces son posibles los casos para t :
$$t < 1$$
$$t = 1$$
Consideremos todos los casos con detalles:
Con
$$t < 1$$
la ecuación será
$$\tilde{\infty} y + \begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} = 0$$
su solución
Con
$$t = 1$$
la ecuación será
$$- 2 x \sin{\left(1 \right)} + \begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} = 0$$
su solución
$$\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} = 2 x \sin{\left(t \right)} + y \log{\left(t \right)}$$
Коэффициент при y равен
$$- \log{\left(t \right)}$$
entonces son posibles los casos para t :
$$t < 1$$
$$t = 1$$
Consideremos todos los casos con detalles:
Con
$$t < 1$$
la ecuación será
$$\tilde{\infty} y + \begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} = 0$$
su solución
Con
$$t = 1$$
la ecuación será
$$- 2 x \sin{\left(1 \right)} + \begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} = 0$$
su solución
Gráfica
Suma y producto de raíces
[src]
suma
/ (1 - 2*re(x*sin(t)))*arg(t) 2*im(x*sin(t))*log(|t|)\ (1 - 2*re(x*sin(t)))*log(|t|) 2*arg(t)*im(x*sin(t)) I*|- --------------------------- - -----------------------| + ----------------------------- - --------------------- | 2 2 2 2 | 2 2 2 2 \ arg (t) + log (|t|) arg (t) + log (|t|) / arg (t) + log (|t|) arg (t) + log (|t|)
$$\frac{\left(1 - 2 \operatorname{re}{\left(x \sin{\left(t \right)}\right)}\right) \log{\left(\left|{t}\right| \right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}} + i \left(- \frac{\left(1 - 2 \operatorname{re}{\left(x \sin{\left(t \right)}\right)}\right) \arg{\left(t \right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}} - \frac{2 \log{\left(\left|{t}\right| \right)} \operatorname{im}{\left(x \sin{\left(t \right)}\right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}}\right) - \frac{2 \operatorname{im}{\left(x \sin{\left(t \right)}\right)} \arg{\left(t \right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}}$$
=
/ (1 - 2*re(x*sin(t)))*arg(t) 2*im(x*sin(t))*log(|t|)\ (1 - 2*re(x*sin(t)))*log(|t|) 2*arg(t)*im(x*sin(t)) I*|- --------------------------- - -----------------------| + ----------------------------- - --------------------- | 2 2 2 2 | 2 2 2 2 \ arg (t) + log (|t|) arg (t) + log (|t|) / arg (t) + log (|t|) arg (t) + log (|t|)
$$\frac{\left(1 - 2 \operatorname{re}{\left(x \sin{\left(t \right)}\right)}\right) \log{\left(\left|{t}\right| \right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}} + i \left(- \frac{\left(1 - 2 \operatorname{re}{\left(x \sin{\left(t \right)}\right)}\right) \arg{\left(t \right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}} - \frac{2 \log{\left(\left|{t}\right| \right)} \operatorname{im}{\left(x \sin{\left(t \right)}\right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}}\right) - \frac{2 \operatorname{im}{\left(x \sin{\left(t \right)}\right)} \arg{\left(t \right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}}$$
producto
/ (1 - 2*re(x*sin(t)))*arg(t) 2*im(x*sin(t))*log(|t|)\ (1 - 2*re(x*sin(t)))*log(|t|) 2*arg(t)*im(x*sin(t)) I*|- --------------------------- - -----------------------| + ----------------------------- - --------------------- | 2 2 2 2 | 2 2 2 2 \ arg (t) + log (|t|) arg (t) + log (|t|) / arg (t) + log (|t|) arg (t) + log (|t|)
$$\frac{\left(1 - 2 \operatorname{re}{\left(x \sin{\left(t \right)}\right)}\right) \log{\left(\left|{t}\right| \right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}} + i \left(- \frac{\left(1 - 2 \operatorname{re}{\left(x \sin{\left(t \right)}\right)}\right) \arg{\left(t \right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}} - \frac{2 \log{\left(\left|{t}\right| \right)} \operatorname{im}{\left(x \sin{\left(t \right)}\right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}}\right) - \frac{2 \operatorname{im}{\left(x \sin{\left(t \right)}\right)} \arg{\left(t \right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}}$$
=
I*((-1 + 2*re(x*sin(t)))*arg(t) - 2*im(x*sin(t))*log(|t|)) - (-1 + 2*re(x*sin(t)))*log(|t|) - 2*arg(t)*im(x*sin(t))
-------------------------------------------------------------------------------------------------------------------
2 2
arg (t) + log (|t|)
$$\frac{i \left(\left(2 \operatorname{re}{\left(x \sin{\left(t \right)}\right)} - 1\right) \arg{\left(t \right)} - 2 \log{\left(\left|{t}\right| \right)} \operatorname{im}{\left(x \sin{\left(t \right)}\right)}\right) - \left(2 \operatorname{re}{\left(x \sin{\left(t \right)}\right)} - 1\right) \log{\left(\left|{t}\right| \right)} - 2 \operatorname{im}{\left(x \sin{\left(t \right)}\right)} \arg{\left(t \right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}}$$
(i*((-1 + 2*re(x*sin(t)))*arg(t) - 2*im(x*sin(t))*log(|t|)) - (-1 + 2*re(x*sin(t)))*log(|t|) - 2*arg(t)*im(x*sin(t)))/(arg(t)^2 + log(|t|)^2)
Respuesta rápida
[src]
/ (1 - 2*re(x*sin(t)))*arg(t) 2*im(x*sin(t))*log(|t|)\ (1 - 2*re(x*sin(t)))*log(|t|) 2*arg(t)*im(x*sin(t))
y1 = I*|- --------------------------- - -----------------------| + ----------------------------- - ---------------------
| 2 2 2 2 | 2 2 2 2
\ arg (t) + log (|t|) arg (t) + log (|t|) / arg (t) + log (|t|) arg (t) + log (|t|)
$$y_{1} = \frac{\left(1 - 2 \operatorname{re}{\left(x \sin{\left(t \right)}\right)}\right) \log{\left(\left|{t}\right| \right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}} + i \left(- \frac{\left(1 - 2 \operatorname{re}{\left(x \sin{\left(t \right)}\right)}\right) \arg{\left(t \right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}} - \frac{2 \log{\left(\left|{t}\right| \right)} \operatorname{im}{\left(x \sin{\left(t \right)}\right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}}\right) - \frac{2 \operatorname{im}{\left(x \sin{\left(t \right)}\right)} \arg{\left(t \right)}}{\log{\left(\left|{t}\right| \right)}^{2} + \arg^{2}{\left(t \right)}}$$
y1 = (1 - 2*re(x*sin(t)))*log(|t|)/(log(|t|)^2 + arg(t)^2) + i*(-(1 - 2*re(x*sin(t)))*arg(t)/(log(|t|)^2 + arg(t)^2) - 2*log(|t|)*im(x*sin(t))/(log(|t|)^2 + arg(t)^2)) - 2*im(x*sin(t))*arg(t)/(log(|t|)^2 + arg(t)^2)