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Otras calculadoras
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- La ecuación:
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Ecuación 3*x^2-x+2=0
-
Ecuación 1-x/2=x/3
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Ecuación 3*x^2-9=0
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Ecuación 0,084:(6,2-x)=1,2
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- -17*x+2*y=9
- 10*x-15*y=16
- Derivada de:
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y^1
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Expresiones idénticas
- y^ uno =c+log(x^ dos + dos)
- y en el grado 1 es igual a c más logaritmo de (x al cuadrado más 2)
- y en el grado uno es igual a c más logaritmo de (x en el grado dos más dos)
- y1=c+log(x2+2)
- y1=c+logx2+2
- y^1=c+log(x²+2)
- y en el grado 1=c+log(x en el grado 2+2)
- y^1=c+logx^2+2
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Expresiones semejantes
- y^1=c-log(x^2+2)
- y^1=c+log(x^2-2)
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Expresiones con funciones
- Logaritmo log
- log2x+2(25)=2
- log(1/2)*x=2*x+5
- log(x+1)((x-1)(x^2+x-8))=log(x-1)((x+1)^3)
- log(x)/log(4)=16
- log_2^2(x)-5*log_2(x)+6=0
y^1=c+log(x^2+2) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Gráfica
Respuesta rápida
[src]
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/ 2 / / -re(c) + re(y) -re(c) + re(y)\\ / 2 / / -re(c) + re(y) -re(c) + re(y)\\
4 / / -re(c) + re(y)\ 2 -2*re(c) + 2*re(y) |atan2\-e *sin(-im(y) + im(c)), -2 + cos(-im(y) + im(c))*e /| 4 / / -re(c) + re(y)\ 2 -2*re(c) + 2*re(y) |atan2\-e *sin(-im(y) + im(c)), -2 + cos(-im(y) + im(c))*e /|
x1 = - \/ \-2 + cos(-im(y) + im(c))*e / + sin (-im(y) + im(c))*e *cos|-------------------------------------------------------------------------------------| - I*\/ \-2 + cos(-im(y) + im(c))*e / + sin (-im(y) + im(c))*e *sin|-------------------------------------------------------------------------------------|
\ 2 / \ 2 /
$$x_{1} = - i \sqrt[4]{\left(e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2\right)^{2} + e^{- 2 \operatorname{re}{\left(c\right)} + 2 \operatorname{re}{\left(y\right)}} \sin^{2}{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)},e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2 \right)}}{2} \right)} - \sqrt[4]{\left(e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2\right)^{2} + e^{- 2 \operatorname{re}{\left(c\right)} + 2 \operatorname{re}{\left(y\right)}} \sin^{2}{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)},e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2 \right)}}{2} \right)}$$
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/ 2 / / -re(c) + re(y) -re(c) + re(y)\\ / 2 / / -re(c) + re(y) -re(c) + re(y)\\
4 / / -re(c) + re(y)\ 2 -2*re(c) + 2*re(y) |atan2\-e *sin(-im(y) + im(c)), -2 + cos(-im(y) + im(c))*e /| 4 / / -re(c) + re(y)\ 2 -2*re(c) + 2*re(y) |atan2\-e *sin(-im(y) + im(c)), -2 + cos(-im(y) + im(c))*e /|
x2 = \/ \-2 + cos(-im(y) + im(c))*e / + sin (-im(y) + im(c))*e *cos|-------------------------------------------------------------------------------------| + I*\/ \-2 + cos(-im(y) + im(c))*e / + sin (-im(y) + im(c))*e *sin|-------------------------------------------------------------------------------------|
\ 2 / \ 2 /
$$x_{2} = i \sqrt[4]{\left(e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2\right)^{2} + e^{- 2 \operatorname{re}{\left(c\right)} + 2 \operatorname{re}{\left(y\right)}} \sin^{2}{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)},e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2 \right)}}{2} \right)} + \sqrt[4]{\left(e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2\right)^{2} + e^{- 2 \operatorname{re}{\left(c\right)} + 2 \operatorname{re}{\left(y\right)}} \sin^{2}{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)},e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2 \right)}}{2} \right)}$$
x2 = i*((exp(-re(c) + re(y))*cos(im(c) - im(y)) - 2)^2 + exp(-2*re(c) + 2*re(y))*sin(im(c) - im(y))^2)^(1/4)*sin(atan2(-exp(-re(c) + re(y))*sin(im(c) - im(y), exp(-re(c) + re(y))*cos(im(c) - im(y)) - 2)/2) + ((exp(-re(c) + re(y))*cos(im(c) - im(y)) - 2)^2 + exp(-2*re(c) + 2*re(y))*sin(im(c) - im(y))^2)^(1/4)*cos(atan2(-exp(-re(c) + re(y))*sin(im(c) - im(y)), exp(-re(c) + re(y))*cos(im(c) - im(y)) - 2)/2))
Suma y producto de raíces
[src]
suma
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/ 2 / / -re(c) + re(y) -re(c) + re(y)\\ / 2 / / -re(c) + re(y) -re(c) + re(y)\\ / 2 / / -re(c) + re(y) -re(c) + re(y)\\ / 2 / / -re(c) + re(y) -re(c) + re(y)\\
4 / / -re(c) + re(y)\ 2 -2*re(c) + 2*re(y) |atan2\-e *sin(-im(y) + im(c)), -2 + cos(-im(y) + im(c))*e /| 4 / / -re(c) + re(y)\ 2 -2*re(c) + 2*re(y) |atan2\-e *sin(-im(y) + im(c)), -2 + cos(-im(y) + im(c))*e /| 4 / / -re(c) + re(y)\ 2 -2*re(c) + 2*re(y) |atan2\-e *sin(-im(y) + im(c)), -2 + cos(-im(y) + im(c))*e /| 4 / / -re(c) + re(y)\ 2 -2*re(c) + 2*re(y) |atan2\-e *sin(-im(y) + im(c)), -2 + cos(-im(y) + im(c))*e /|
- \/ \-2 + cos(-im(y) + im(c))*e / + sin (-im(y) + im(c))*e *cos|-------------------------------------------------------------------------------------| - I*\/ \-2 + cos(-im(y) + im(c))*e / + sin (-im(y) + im(c))*e *sin|-------------------------------------------------------------------------------------| + \/ \-2 + cos(-im(y) + im(c))*e / + sin (-im(y) + im(c))*e *cos|-------------------------------------------------------------------------------------| + I*\/ \-2 + cos(-im(y) + im(c))*e / + sin (-im(y) + im(c))*e *sin|-------------------------------------------------------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(- i \sqrt[4]{\left(e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2\right)^{2} + e^{- 2 \operatorname{re}{\left(c\right)} + 2 \operatorname{re}{\left(y\right)}} \sin^{2}{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)},e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2 \right)}}{2} \right)} - \sqrt[4]{\left(e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2\right)^{2} + e^{- 2 \operatorname{re}{\left(c\right)} + 2 \operatorname{re}{\left(y\right)}} \sin^{2}{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)},e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2 \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2\right)^{2} + e^{- 2 \operatorname{re}{\left(c\right)} + 2 \operatorname{re}{\left(y\right)}} \sin^{2}{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)},e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2 \right)}}{2} \right)} + \sqrt[4]{\left(e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2\right)^{2} + e^{- 2 \operatorname{re}{\left(c\right)} + 2 \operatorname{re}{\left(y\right)}} \sin^{2}{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)},e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2 \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ ________________________________________________________________________________________ ________________________________________________________________________________________ \ / ________________________________________________________________________________________ ________________________________________________________________________________________ \ | / 2 / / -re(c) + re(y) -re(c) + re(y)\\ / 2 / / -re(c) + re(y) -re(c) + re(y)\\| | / 2 / / -re(c) + re(y) -re(c) + re(y)\\ / 2 / / -re(c) + re(y) -re(c) + re(y)\\| | 4 / / -re(c) + re(y)\ 2 -2*re(c) + 2*re(y) |atan2\-e *sin(-im(y) + im(c)), -2 + cos(-im(y) + im(c))*e /| 4 / / -re(c) + re(y)\ 2 -2*re(c) + 2*re(y) |atan2\-e *sin(-im(y) + im(c)), -2 + cos(-im(y) + im(c))*e /|| |4 / / -re(c) + re(y)\ 2 -2*re(c) + 2*re(y) |atan2\-e *sin(-im(y) + im(c)), -2 + cos(-im(y) + im(c))*e /| 4 / / -re(c) + re(y)\ 2 -2*re(c) + 2*re(y) |atan2\-e *sin(-im(y) + im(c)), -2 + cos(-im(y) + im(c))*e /|| |- \/ \-2 + cos(-im(y) + im(c))*e / + sin (-im(y) + im(c))*e *cos|-------------------------------------------------------------------------------------| - I*\/ \-2 + cos(-im(y) + im(c))*e / + sin (-im(y) + im(c))*e *sin|-------------------------------------------------------------------------------------||*|\/ \-2 + cos(-im(y) + im(c))*e / + sin (-im(y) + im(c))*e *cos|-------------------------------------------------------------------------------------| + I*\/ \-2 + cos(-im(y) + im(c))*e / + sin (-im(y) + im(c))*e *sin|-------------------------------------------------------------------------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(- i \sqrt[4]{\left(e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2\right)^{2} + e^{- 2 \operatorname{re}{\left(c\right)} + 2 \operatorname{re}{\left(y\right)}} \sin^{2}{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)},e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2 \right)}}{2} \right)} - \sqrt[4]{\left(e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2\right)^{2} + e^{- 2 \operatorname{re}{\left(c\right)} + 2 \operatorname{re}{\left(y\right)}} \sin^{2}{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)},e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2 \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2\right)^{2} + e^{- 2 \operatorname{re}{\left(c\right)} + 2 \operatorname{re}{\left(y\right)}} \sin^{2}{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)},e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2 \right)}}{2} \right)} + \sqrt[4]{\left(e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2\right)^{2} + e^{- 2 \operatorname{re}{\left(c\right)} + 2 \operatorname{re}{\left(y\right)}} \sin^{2}{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)},e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} - 2 \right)}}{2} \right)}\right)$$
=
/ / I*(-im(y) + im(c)) -I*(-im(y) + im(c))\ -re(c) + re(y) / I*(-im(y) + im(c)) -I*(-im(y) + im(c))\ \
|-I*\- e + e /*e |e e | -re(c) + re(y)|
_________________________________________________________________ I*atan2|------------------------------------------------------------------, -2 + |------------------- + --------------------|*e |
/ -re(c) + re(y) -2*re(c) + 2*re(y) \ 2 \ 2 2 / /
-\/ 4 - 4*cos(-im(y) + im(c))*e + e *e
$$- \sqrt{e^{- 2 \operatorname{re}{\left(c\right)} + 2 \operatorname{re}{\left(y\right)}} - 4 e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)} \right)} + 4} e^{i \operatorname{atan_{2}}{\left(- \frac{i \left(- e^{i \left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)}\right)} + e^{- i \left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)}\right)}\right) e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}}}{2},\left(\frac{e^{i \left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)}\right)}}{2} + \frac{e^{- i \left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(y\right)}\right)}}{2}\right) e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(y\right)}} - 2 \right)}}$$
-sqrt(4 - 4*cos(-im(y) + im(c))*exp(-re(c) + re(y)) + exp(-2*re(c) + 2*re(y)))*exp(i*atan2(-i*(-exp(i*(-im(y) + im(c))) + exp(-i*(-im(y) + im(c))))*exp(-re(c) + re(y))/2, -2 + (exp(i*(-im(y) + im(c)))/2 + exp(-i*(-im(y) + im(c)))/2)*exp(-re(c) + re(y))))