Sr Examen

Lang:

Otras calculadoras

¿Cómo usar?
La ecuación:
Ecuación x=x/2+1
Ecuación cos(x)=sqrt(3)/2
Ecuación tan(x)=1
Ecuación x^2-7x+10=0
Expresar {x} en función de y en la ecuación:
18*x-12*y=-20
2*x+18*y=20
(x^2+1)/(x2-1)=y
-4*x+18*y=-14
Forma canónica:
xy+xz+yz
Expresión:
xy+xz+yz
Expresiones idénticas
xy+xz+yz= treinta -x^ dos
xy más xz más yz es igual a 30 menos x al cuadrado
xy más xz más yz es igual a treinta menos x en el grado dos
xy+xz+yz=30-x2
xy+xz+yz=30-x²
xy+xz+yz=30-x en el grado 2
Expresiones semejantes
xy+xz-yz=30-x^2
xy-xz+yz=30-x^2
xy+xz+yz=30+x^2
Expresiones con funciones
xy
xy−3x+2y=12
xy-y=0
xy-3y=-1
xy+48y=10,2
xysin(x)x
xz
xz
xz+x=36

xy+xz+yz=30-x^2 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

                        2
x*y + x*z + y*z = 30 - x

y z + \left(x y + x z\right) = 30 - x^{2}

Simplificar

Solución detallada

Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.

La ecuación se convierte de

y z + \left(x y + x z\right) = 30 - x^{2}

\left(x^{2} - 30\right) + \left(y z + \left(x y + x z\right)\right) = 0

Es la ecuación de la forma

a*x^2 + b*x + c = 0

La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:

x_{1} = \frac{\sqrt{D} - b}{2 a}

x_{2} = \frac{- \sqrt{D} - b}{2 a}

donde D = b^2 - 4*a*c es el discriminante.
Como

a = 1

b = y + z

c = y z - 30

, entonces

D = b^2 - 4 * a * c =

(y + z)^2 - 4 * (1) * (-30 + y*z) = 120 + (y + z)^2 - 4*y*z

La ecuación tiene dos raíces.

x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

x_{1} = - \frac{y}{2} - \frac{z}{2} + \frac{\sqrt{- 4 y z + \left(y + z\right)^{2} + 120}}{2}

x_{2} = - \frac{y}{2} - \frac{z}{2} - \frac{\sqrt{- 4 y z + \left(y + z\right)^{2} + 120}}{2}

Teorema de Cardano-Vieta

es ecuación cuadrática reducida

p x + q + x^{2} = 0

donde

p = \frac{b}{a}

p = y + z

q = \frac{c}{a}

q = y z - 30

Fórmulas de Cardano-Vieta

x_{1} + x_{2} = - p

x_{1} x_{2} = q

x_{1} + x_{2} = - y - z

x_{1} x_{2} = y z - 30

Gráfica

Respuesta rápida [src]

                         /                      ________________________________________________________________________________________________________                                                                                                            \       ________________________________________________________________________________________________________                                                                                                            
                         |                     /                                                                                                      2     /     /                                                    2        2        2        2               \\|      /                                                                                                      2     /     /                                                    2        2        2        2               \\
                         |                  4 /                                              2   /        2        2        2        2               \      |atan2\-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z), 120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/||   4 /                                              2   /        2        2        2        2               \      |atan2\-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z), 120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/|
                         |                  \/   (-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z))  + \120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/  *sin|------------------------------------------------------------------------------------------------------||   \/   (-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z))  + \120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/  *cos|------------------------------------------------------------------------------------------------------|
       re(y)   re(z)     |  im(y)   im(z)                                                                                                                   \                                                  2                                                   /|                                                                                                                   \                                                  2                                                   /
x1 = - ----- - ----- + I*|- ----- - ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
         2       2       \    2       2                                                                                                                2                                                                                                            /                                                                                                              2

x_{1} = - \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120 \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2} - \frac{\operatorname{im}{\left(z\right)}}{2}\right) - \frac{\operatorname{re}{\left(y\right)}}{2} - \frac{\operatorname{re}{\left(z\right)}}{2}

                         /                      ________________________________________________________________________________________________________                                                                                                            \       ________________________________________________________________________________________________________                                                                                                            
                         |                     /                                                                                                      2     /     /                                                    2        2        2        2               \\|      /                                                                                                      2     /     /                                                    2        2        2        2               \\
                         |                  4 /                                              2   /        2        2        2        2               \      |atan2\-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z), 120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/||   4 /                                              2   /        2        2        2        2               \      |atan2\-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z), 120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/|
                         |                  \/   (-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z))  + \120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/  *sin|------------------------------------------------------------------------------------------------------||   \/   (-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z))  + \120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/  *cos|------------------------------------------------------------------------------------------------------|
       re(y)   re(z)     |  im(y)   im(z)                                                                                                                   \                                                  2                                                   /|                                                                                                                   \                                                  2                                                   /
x2 = - ----- - ----- + I*|- ----- - ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
         2       2       \    2       2                                                                                                                2                                                                                                            /                                                                                                              2

x_{2} = \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120 \right)}}{2} \right)}}{2} + i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2} - \frac{\operatorname{im}{\left(z\right)}}{2}\right) - \frac{\operatorname{re}{\left(y\right)}}{2} - \frac{\operatorname{re}{\left(z\right)}}{2}

x2 = ((2*re(y)*im(y) + 2*re(z)*im(z) - 2*im(y*z))^2 + (re(y)^2 + re(z)^2 - 2*re(y*z) - im(y)^2 - im(z)^2 + 120)^2)^(1/4)*cos(atan2(2*re(y)*im(y) + 2*re(z)*im(z) - 2*im(y*z, re(y)^2 + re(z)^2 - 2*re(y*z) - im(y)^2 - im(z)^2 + 120)/2)/2 + i*(((2*re(y)*im(y) + 2*re(z)*im(z) - 2*im(y*z))^2 + (re(y)^2 + re(z)^2 - 2*re(y*z) - im(y)^2 - im(z)^2 + 120)^2)^(1/4)*sin(atan2(2*re(y)*im(y) + 2*re(z)*im(z) - 2*im(y*z), re(y)^2 + re(z)^2 - 2*re(y*z) - im(y)^2 - im(z)^2 + 120)/2)/2 - im(y)/2 - im(z)/2) - re(y)/2 - re(z)/2)

Suma y producto de raíces [src]

suma

                    /                      ________________________________________________________________________________________________________                                                                                                            \       ________________________________________________________________________________________________________                                                                                                                                   /                      ________________________________________________________________________________________________________                                                                                                            \       ________________________________________________________________________________________________________                                                                                                            
                    |                     /                                                                                                      2     /     /                                                    2        2        2        2               \\|      /                                                                                                      2     /     /                                                    2        2        2        2               \\                       |                     /                                                                                                      2     /     /                                                    2        2        2        2               \\|      /                                                                                                      2     /     /                                                    2        2        2        2               \\
                    |                  4 /                                              2   /        2        2        2        2               \      |atan2\-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z), 120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/||   4 /                                              2   /        2        2        2        2               \      |atan2\-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z), 120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/|                       |                  4 /                                              2   /        2        2        2        2               \      |atan2\-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z), 120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/||   4 /                                              2   /        2        2        2        2               \      |atan2\-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z), 120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/|
                    |                  \/   (-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z))  + \120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/  *sin|------------------------------------------------------------------------------------------------------||   \/   (-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z))  + \120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/  *cos|------------------------------------------------------------------------------------------------------|                       |                  \/   (-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z))  + \120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/  *sin|------------------------------------------------------------------------------------------------------||   \/   (-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z))  + \120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/  *cos|------------------------------------------------------------------------------------------------------|
  re(y)   re(z)     |  im(y)   im(z)                                                                                                                   \                                                  2                                                   /|                                                                                                                   \                                                  2                                                   /     re(y)   re(z)     |  im(y)   im(z)                                                                                                                   \                                                  2                                                   /|                                                                                                                   \                                                  2                                                   /
- ----- - ----- + I*|- ----- - ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + - ----- - ----- + I*|- ----- - ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
    2       2       \    2       2                                                                                                                2                                                                                                            /                                                                                                              2                                                                                                                   2       2       \    2       2                                                                                                                2                                                                                                            /                                                                                                              2

\left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120 \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2} - \frac{\operatorname{im}{\left(z\right)}}{2}\right) - \frac{\operatorname{re}{\left(y\right)}}{2} - \frac{\operatorname{re}{\left(z\right)}}{2}\right) + \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120 \right)}}{2} \right)}}{2} + i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2} - \frac{\operatorname{im}{\left(z\right)}}{2}\right) - \frac{\operatorname{re}{\left(y\right)}}{2} - \frac{\operatorname{re}{\left(z\right)}}{2}\right)

                   /                      ________________________________________________________________________________________________________                                                                                                            \     /                      ________________________________________________________________________________________________________                                                                                                            \
                   |                     /                                                                                                      2     /     /                                                    2        2        2        2               \\|     |                     /                                                                                                      2     /     /                                                    2        2        2        2               \\|
                   |                  4 /                                              2   /        2        2        2        2               \      |atan2\-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z), 120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/||     |                  4 /                                              2   /        2        2        2        2               \      |atan2\-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z), 120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/||
                   |                  \/   (-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z))  + \120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/  *sin|------------------------------------------------------------------------------------------------------||     |                  \/   (-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z))  + \120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/  *sin|------------------------------------------------------------------------------------------------------||
                   |  im(y)   im(z)                                                                                                                   \                                                  2                                                   /|     |  im(y)   im(z)                                                                                                                   \                                                  2                                                   /|
-re(y) - re(z) + I*|- ----- - ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|- ----- - ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
                   \    2       2                                                                                                                2                                                                                                            /     \    2       2                                                                                                                2                                                                                                            /

i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2} - \frac{\operatorname{im}{\left(z\right)}}{2}\right) + i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2} - \frac{\operatorname{im}{\left(z\right)}}{2}\right) - \operatorname{re}{\left(y\right)} - \operatorname{re}{\left(z\right)}

producto

/                    /                      ________________________________________________________________________________________________________                                                                                                            \       ________________________________________________________________________________________________________                                                                                                            \ /                    /                      ________________________________________________________________________________________________________                                                                                                            \       ________________________________________________________________________________________________________                                                                                                            \
|                    |                     /                                                                                                      2     /     /                                                    2        2        2        2               \\|      /                                                                                                      2     /     /                                                    2        2        2        2               \\| |                    |                     /                                                                                                      2     /     /                                                    2        2        2        2               \\|      /                                                                                                      2     /     /                                                    2        2        2        2               \\|
|                    |                  4 /                                              2   /        2        2        2        2               \      |atan2\-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z), 120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/||   4 /                                              2   /        2        2        2        2               \      |atan2\-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z), 120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/|| |                    |                  4 /                                              2   /        2        2        2        2               \      |atan2\-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z), 120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/||   4 /                                              2   /        2        2        2        2               \      |atan2\-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z), 120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/||
|                    |                  \/   (-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z))  + \120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/  *sin|------------------------------------------------------------------------------------------------------||   \/   (-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z))  + \120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/  *cos|------------------------------------------------------------------------------------------------------|| |                    |                  \/   (-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z))  + \120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/  *sin|------------------------------------------------------------------------------------------------------||   \/   (-2*im(y*z) + 2*im(y)*re(y) + 2*im(z)*re(z))  + \120 + re (y) + re (z) - im (y) - im (z) - 2*re(y*z)/  *cos|------------------------------------------------------------------------------------------------------||
|  re(y)   re(z)     |  im(y)   im(z)                                                                                                                   \                                                  2                                                   /|                                                                                                                   \                                                  2                                                   /| |  re(y)   re(z)     |  im(y)   im(z)                                                                                                                   \                                                  2                                                   /|                                                                                                                   \                                                  2                                                   /|
|- ----- - ----- + I*|- ----- - ----- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|- ----- - ----- + I*|- ----- - ----- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\    2       2       \    2       2                                                                                                                2                                                                                                            /                                                                                                              2                                                                                                            / \    2       2       \    2       2                                                                                                                2                                                                                                            /                                                                                                              2                                                                                                            /

\left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120 \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2} - \frac{\operatorname{im}{\left(z\right)}}{2}\right) - \frac{\operatorname{re}{\left(y\right)}}{2} - \frac{\operatorname{re}{\left(z\right)}}{2}\right) \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120 \right)}}{2} \right)}}{2} + i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 2 \operatorname{im}{\left(y z\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(z\right)}\right)^{2} - 2 \operatorname{re}{\left(y z\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(z\right)}\right)^{2} + 120 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2} - \frac{\operatorname{im}{\left(z\right)}}{2}\right) - \frac{\operatorname{re}{\left(y\right)}}{2} - \frac{\operatorname{re}{\left(z\right)}}{2}\right)

      re(y*z)   I*im(y*z)   re(y)*re(z)   im(y)*im(z)   I*im(y)*re(z)   I*im(z)*re(y)
-30 + ------- + --------- + ----------- - ----------- + ------------- + -------------
         2          2            2             2              2               2

\frac{\operatorname{re}{\left(y\right)} \operatorname{re}{\left(z\right)}}{2} + \frac{i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(z\right)}}{2} + \frac{i \operatorname{re}{\left(z\right)} \operatorname{im}{\left(y\right)}}{2} + \frac{\operatorname{re}{\left(y z\right)}}{2} - \frac{\operatorname{im}{\left(y\right)} \operatorname{im}{\left(z\right)}}{2} + \frac{i \operatorname{im}{\left(y z\right)}}{2} - 30

-30 + re(y*z)/2 + i*im(y*z)/2 + re(y)*re(z)/2 - im(y)*im(z)/2 + i*im(y)*re(z)/2 + i*im(z)*re(y)/2

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

xy+xz+yz=30-x^2 la ecuación

Solución numérica:

Solución