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- La ecuación:
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Ecuación x/3+x/4=-21
-
Ecuación 3^x=4
-
Ecuación 3*x^2=18*x
-
Ecuación x^4-8*x^2+7=0
- Expresar {x} en función de y en la ecuación:
- 11*x-12*y=11
- 8*x-13*y=-12
- 19*x-2*y=-17
- -16*x-12*y=12
-
Expresiones idénticas
- z-log(x^ dos +y^ dos)= cero
- z menos logaritmo de (x al cuadrado más y al cuadrado ) es igual a 0
- z menos logaritmo de (x en el grado dos más y en el grado dos) es igual a cero
- z-log(x2+y2)=0
- z-logx2+y2=0
- z-log(x²+y²)=0
- z-log(x en el grado 2+y en el grado 2)=0
- z-logx^2+y^2=0
- z-log(x^2+y^2)=O
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Expresiones semejantes
- z+log(x^2+y^2)=0
- z-log(x^2-y^2)=0
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Expresiones con funciones
- Logaritmo log
- log(c)=0
- Log[2,34-2^x]=2-Sqrt[x-4]=0
- log(z)=log(20^(1/2))+(-atan((2)+2*pi*m))*i
- log2x-5log2x=0
- log(x)=x+45*gamma(x)
z-log(x^2+y^2)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Gráfica
Suma y producto de raíces
[src]
suma
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/ 2 2 / / re(z) 2 2 re(z)\\ / 2 2 / / re(z) 2 2 re(z)\\ / 2 2 / / re(z) 2 2 re(z)\\ / 2 2 / / re(z) 2 2 re(z)\\
4 / / re(z) \ / 2 2 re(z)\ |atan2\e *sin(im(z)) - 2*im(y)*re(y), im (y) - re (y) + cos(im(z))*e /| 4 / / re(z) \ / 2 2 re(z)\ |atan2\e *sin(im(z)) - 2*im(y)*re(y), im (y) - re (y) + cos(im(z))*e /| 4 / / re(z) \ / 2 2 re(z)\ |atan2\e *sin(im(z)) - 2*im(y)*re(y), im (y) - re (y) + cos(im(z))*e /| 4 / / re(z) \ / 2 2 re(z)\ |atan2\e *sin(im(z)) - 2*im(y)*re(y), im (y) - re (y) + cos(im(z))*e /|
- \/ \e *sin(im(z)) - 2*im(y)*re(y)/ + \im (y) - re (y) + cos(im(z))*e / *cos|-----------------------------------------------------------------------------| - I*\/ \e *sin(im(z)) - 2*im(y)*re(y)/ + \im (y) - re (y) + cos(im(z))*e / *sin|-----------------------------------------------------------------------------| + \/ \e *sin(im(z)) - 2*im(y)*re(y)/ + \im (y) - re (y) + cos(im(z))*e / *cos|-----------------------------------------------------------------------------| + I*\/ \e *sin(im(z)) - 2*im(y)*re(y)/ + \im (y) - re (y) + cos(im(z))*e / *sin|-----------------------------------------------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(- i \sqrt[4]{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ _______________________________________________________________________________ _______________________________________________________________________________ \ / _______________________________________________________________________________ _______________________________________________________________________________ \ | / 2 2 / / re(z) 2 2 re(z)\\ / 2 2 / / re(z) 2 2 re(z)\\| | / 2 2 / / re(z) 2 2 re(z)\\ / 2 2 / / re(z) 2 2 re(z)\\| | 4 / / re(z) \ / 2 2 re(z)\ |atan2\e *sin(im(z)) - 2*im(y)*re(y), im (y) - re (y) + cos(im(z))*e /| 4 / / re(z) \ / 2 2 re(z)\ |atan2\e *sin(im(z)) - 2*im(y)*re(y), im (y) - re (y) + cos(im(z))*e /|| |4 / / re(z) \ / 2 2 re(z)\ |atan2\e *sin(im(z)) - 2*im(y)*re(y), im (y) - re (y) + cos(im(z))*e /| 4 / / re(z) \ / 2 2 re(z)\ |atan2\e *sin(im(z)) - 2*im(y)*re(y), im (y) - re (y) + cos(im(z))*e /|| |- \/ \e *sin(im(z)) - 2*im(y)*re(y)/ + \im (y) - re (y) + cos(im(z))*e / *cos|-----------------------------------------------------------------------------| - I*\/ \e *sin(im(z)) - 2*im(y)*re(y)/ + \im (y) - re (y) + cos(im(z))*e / *sin|-----------------------------------------------------------------------------||*|\/ \e *sin(im(z)) - 2*im(y)*re(y)/ + \im (y) - re (y) + cos(im(z))*e / *cos|-----------------------------------------------------------------------------| + I*\/ \e *sin(im(z)) - 2*im(y)*re(y)/ + \im (y) - re (y) + cos(im(z))*e / *sin|-----------------------------------------------------------------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(- i \sqrt[4]{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}\right)$$
=
/ / 2*I*im(z)\ -I*im(z) re(z) / -2*I*im(z)\ I*im(z) re(z)\
_______________________________________________________________________________ | I*\-1 + e /*e *e 2 2 \1 + e /*e *e |
/ 2 2 I*atan2|-2*im(y)*re(y) - ------------------------------------, im (y) - re (y) + ---------------------------------|
/ / re(z) \ / 2 2 re(z)\ \ 2 2 /
-\/ \e *sin(im(z)) - 2*im(y)*re(y)/ + \im (y) - re (y) + cos(im(z))*e / *e
$$- \sqrt{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(- \frac{i \left(e^{2 i \operatorname{im}{\left(z\right)}} - 1\right) e^{- i \operatorname{im}{\left(z\right)}} e^{\operatorname{re}{\left(z\right)}}}{2} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\frac{\left(1 + e^{- 2 i \operatorname{im}{\left(z\right)}}\right) e^{i \operatorname{im}{\left(z\right)}} e^{\operatorname{re}{\left(z\right)}}}{2} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}$$
-sqrt((exp(re(z))*sin(im(z)) - 2*im(y)*re(y))^2 + (im(y)^2 - re(y)^2 + cos(im(z))*exp(re(z)))^2)*exp(i*atan2(-2*im(y)*re(y) - i*(-1 + exp(2*i*im(z)))*exp(-i*im(z))*exp(re(z))/2, im(y)^2 - re(y)^2 + (1 + exp(-2*i*im(z)))*exp(i*im(z))*exp(re(z))/2))
Respuesta rápida
[src]
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/ 2 2 / / re(z) 2 2 re(z)\\ / 2 2 / / re(z) 2 2 re(z)\\
4 / / re(z) \ / 2 2 re(z)\ |atan2\e *sin(im(z)) - 2*im(y)*re(y), im (y) - re (y) + cos(im(z))*e /| 4 / / re(z) \ / 2 2 re(z)\ |atan2\e *sin(im(z)) - 2*im(y)*re(y), im (y) - re (y) + cos(im(z))*e /|
x1 = - \/ \e *sin(im(z)) - 2*im(y)*re(y)/ + \im (y) - re (y) + cos(im(z))*e / *cos|-----------------------------------------------------------------------------| - I*\/ \e *sin(im(z)) - 2*im(y)*re(y)/ + \im (y) - re (y) + cos(im(z))*e / *sin|-----------------------------------------------------------------------------|
\ 2 / \ 2 /
$$x_{1} = - i \sqrt[4]{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}$$
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/ 2 2 / / re(z) 2 2 re(z)\\ / 2 2 / / re(z) 2 2 re(z)\\
4 / / re(z) \ / 2 2 re(z)\ |atan2\e *sin(im(z)) - 2*im(y)*re(y), im (y) - re (y) + cos(im(z))*e /| 4 / / re(z) \ / 2 2 re(z)\ |atan2\e *sin(im(z)) - 2*im(y)*re(y), im (y) - re (y) + cos(im(z))*e /|
x2 = \/ \e *sin(im(z)) - 2*im(y)*re(y)/ + \im (y) - re (y) + cos(im(z))*e / *cos|-----------------------------------------------------------------------------| + I*\/ \e *sin(im(z)) - 2*im(y)*re(y)/ + \im (y) - re (y) + cos(im(z))*e / *sin|-----------------------------------------------------------------------------|
\ 2 / \ 2 /
$$x_{2} = i \sqrt[4]{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(e^{\operatorname{re}{\left(z\right)}} \sin{\left(\operatorname{im}{\left(z\right)} \right)} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},e^{\operatorname{re}{\left(z\right)}} \cos{\left(\operatorname{im}{\left(z\right)} \right)} - \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}$$
x2 = i*((exp(re(z))*sin(im(z)) - 2*re(y)*im(y))^2 + (exp(re(z))*cos(im(z)) - re(y)^2 + im(y)^2)^2)^(1/4)*sin(atan2(exp(re(z))*sin(im(z)) - 2*re(y)*im(y, exp(re(z))*cos(im(z)) - re(y)^2 + im(y)^2)/2) + ((exp(re(z))*sin(im(z)) - 2*re(y)*im(y))^2 + (exp(re(z))*cos(im(z)) - re(y)^2 + im(y)^2)^2)^(1/4)*cos(atan2(exp(re(z))*sin(im(z)) - 2*re(y)*im(y), exp(re(z))*cos(im(z)) - re(y)^2 + im(y)^2)/2))