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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
- (x^ tres +3y)ln(x^ dos -y)
- (x al cubo más 3y)ln(x al cuadrado menos y)
- (x en el grado tres más 3y)ln(x en el grado dos menos y)
- (x3+3y)ln(x2-y)
- x3+3ylnx2-y
- (x³+3y)ln(x²-y)
- (x en el grado 3+3y)ln(x en el grado 2-y)
- x^3+3ylnx^2-y
-
Expresiones semejantes
- (x^3+3y)ln(x^2+y)
- (x^3-3y)ln(x^2-y)
-
Expresiones con funciones
- ln
- ln(x)=-1
- ln(-x+1)
- ln(x)=18,24156
- ln(x^2+1)*1/2=0
- ln*x+(x+1)^3=0
(x^3+3y)ln(x^2-y) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 3 \ / 2 \ \x + 3*y/*log\x - y/ = 0
$$\left(x^{3} + 3 y\right) \log{\left(x^{2} - y \right)} = 0$$
Gráfica
Suma y producto de raíces
[src]
suma
3 / 3 \
re (x) |im (x) 2 | 2 2 2
- ------ + I*|------ - re (x)*im(x)| + im (x)*re(x) + -1 + re (x) - im (x) + 2*I*im(x)*re(x)
3 \ 3 /
$$\left(i \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(x\right)} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{3}}{3}\right) - \frac{\left(\operatorname{re}{\left(x\right)}\right)^{3}}{3} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 i \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)$$
=
3 / 3 \
2 2 re (x) |im (x) 2 | 2
-1 + re (x) - im (x) - ------ + I*|------ - re (x)*im(x)| + im (x)*re(x) + 2*I*im(x)*re(x)
3 \ 3 /
$$i \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(x\right)} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{3}}{3}\right) - \frac{\left(\operatorname{re}{\left(x\right)}\right)^{3}}{3} + \left(\operatorname{re}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 2 i \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1$$
producto
/ 3 / 3 \ \ | re (x) |im (x) 2 | 2 | / 2 2 \ |- ------ + I*|------ - re (x)*im(x)| + im (x)*re(x)|*\-1 + re (x) - im (x) + 2*I*im(x)*re(x)/ \ 3 \ 3 / /
$$\left(i \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(x\right)} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{3}}{3}\right) - \frac{\left(\operatorname{re}{\left(x\right)}\right)^{3}}{3} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 i \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)$$
=
/ 3 2 / 2 2 \ \ / 2 2 \
-\re (x) - 3*im (x)*re(x) + I*\- im (x) + 3*re (x)/*im(x)/*\-1 + re (x) - im (x) + 2*I*im(x)*re(x)/
----------------------------------------------------------------------------------------------------
3
$$- \frac{\left(i \left(3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)} + \left(\operatorname{re}{\left(x\right)}\right)^{3} - 3 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 i \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)}{3}$$
-(re(x)^3 - 3*im(x)^2*re(x) + i*(-im(x)^2 + 3*re(x)^2)*im(x))*(-1 + re(x)^2 - im(x)^2 + 2*i*im(x)*re(x))/3
Respuesta rápida
[src]
3 / 3 \
re (x) |im (x) 2 | 2
y1 = - ------ + I*|------ - re (x)*im(x)| + im (x)*re(x)
3 \ 3 /
$$y_{1} = i \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(x\right)} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{3}}{3}\right) - \frac{\left(\operatorname{re}{\left(x\right)}\right)^{3}}{3} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2}$$
2 2 y2 = -1 + re (x) - im (x) + 2*I*im(x)*re(x)
$$y_{2} = \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 i \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1$$
y2 = re(x)^2 + 2*i*re(x)*im(x) - im(x)^2 - 1