Sr Examen

Lang:

Otras calculadoras

¿Cómo usar?
La ecuación:
Ecuación x+4=0
Ecuación x*(x^2+8*x+16)=5*(x+4)
Ecuación ((57.6/(150-x))^0.15)*((150+x)+10)/171.712=1
Ecuación 9-4x=3x-40
Expresar {x} en función de y en la ecuación:
-18*x-2*y=9
-9*x+1*y=3
9*x+10*y=5
1*x+10*y=-18
Expresiones idénticas
dos *x^ dos - tres *x*y+ cinco *y= cero
2 multiplicar por x al cuadrado menos 3 multiplicar por x multiplicar por y más 5 multiplicar por y es igual a 0
dos multiplicar por x en el grado dos menos tres multiplicar por x multiplicar por y más cinco multiplicar por y es igual a cero
2*x2-3*x*y+5*y=0
2*x²-3*x*y+5*y=0
2*x en el grado 2-3*x*y+5*y=0
2x^2-3xy+5y=0
2x2-3xy+5y=0
2*x^2-3*x*y+5*y=O
Expresiones semejantes
2*x^2-3*x*y-5*y=0
2*x^2+3*x*y+5*y=0

2x^2-3xy+5y=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

   2                  
2*x  - 3*x*y + 5*y = 0

5 y + \left(2 x^{2} - 3 x y\right) = 0

Simplificar

Solución detallada

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 = 2

b = - 3 y

c = 5 y

, entonces

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

(-3*y)^2 - 4 * (2) * (5*y) = -40*y + 9*y^2

La ecuación tiene dos raíces.

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

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

x_{1} = \frac{3 y}{4} + \frac{\sqrt{9 y^{2} - 40 y}}{4}

x_{2} = \frac{3 y}{4} - \frac{\sqrt{9 y^{2} - 40 y}}{4}

Teorema de Cardano-Vieta

reescribamos la ecuación

5 y + \left(2 x^{2} - 3 x y\right) = 0

a x^{2} + b x + c = 0

como ecuación cuadrática reducida

x^{2} + \frac{b x}{a} + \frac{c}{a} = 0

x^{2} - \frac{3 x y}{2} + \frac{5 y}{2} = 0

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

donde

p = \frac{b}{a}

p = - \frac{3 y}{2}

q = \frac{c}{a}

q = \frac{5 y}{2}

Fórmulas de Cardano-Vieta

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

x_{1} x_{2} = q

x_{1} + x_{2} = \frac{3 y}{2}

x_{1} x_{2} = \frac{5 y}{2}

Gráfica

Suma y producto de raíces [src]

suma

            /              __________________________________________________________________________________                                                                                      \       __________________________________________________________________________________                                                                                                     /              __________________________________________________________________________________                                                                                      \       __________________________________________________________________________________                                                                                      
            |             /                                     2                                                /     /                                             2                           \\|      /                                     2                                                /     /                                             2                           \\               |             /                                     2                                                /     /                                             2                           \\|      /                                     2                                                /     /                                             2                           \\
            |          4 /  /      2                           \                                           2     |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/||   4 /  /      2                           \                                           2     |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|               |          4 /  /      2                           \                                           2     |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/||   4 /  /      2                           \                                           2     |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|
            |          \/   \- 9*im (y) + (-40 + 9*re(y))*re(y)/  + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y))  *sin|--------------------------------------------------------------------------------||   \/   \- 9*im (y) + (-40 + 9*re(y))*re(y)/  + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y))  *cos|--------------------------------------------------------------------------------|               |          \/   \- 9*im (y) + (-40 + 9*re(y))*re(y)/  + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y))  *sin|--------------------------------------------------------------------------------||   \/   \- 9*im (y) + (-40 + 9*re(y))*re(y)/  + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y))  *cos|--------------------------------------------------------------------------------|
3*re(y)     |3*im(y)                                                                                             \                                       2                                        /|                                                                                             \                                       2                                        /   3*re(y)     |3*im(y)                                                                                             \                                       2                                        /|                                                                                             \                                       2                                        /
------- + I*|------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------- + I*|------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
   4        \   4                                                                                           4                                                                                      /                                                                                        4                                                                                            4        \   4                                                                                           4                                                                                      /                                                                                        4

\left(i \left(- \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) - \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{re}{\left(y\right)}}{4}\right) + \left(i \left(\frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) + \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{re}{\left(y\right)}}{4}\right)

            /              __________________________________________________________________________________                                                                                      \     /              __________________________________________________________________________________                                                                                      \
            |             /                                     2                                                /     /                                             2                           \\|     |             /                                     2                                                /     /                                             2                           \\|
            |          4 /  /      2                           \                                           2     |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/||     |          4 /  /      2                           \                                           2     |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/||
            |          \/   \- 9*im (y) + (-40 + 9*re(y))*re(y)/  + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y))  *sin|--------------------------------------------------------------------------------||     |          \/   \- 9*im (y) + (-40 + 9*re(y))*re(y)/  + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y))  *sin|--------------------------------------------------------------------------------||
3*re(y)     |3*im(y)                                                                                             \                                       2                                        /|     |3*im(y)                                                                                             \                                       2                                        /|
------- + I*|------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
   2        \   4                                                                                           4                                                                                      /     \   4                                                                                           4                                                                                      /

i \left(- \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) + i \left(\frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) + \frac{3 \operatorname{re}{\left(y\right)}}{2}

producto

/            /              __________________________________________________________________________________                                                                                      \       __________________________________________________________________________________                                                                                      \ /            /              __________________________________________________________________________________                                                                                      \       __________________________________________________________________________________                                                                                      \
|            |             /                                     2                                                /     /                                             2                           \\|      /                                     2                                                /     /                                             2                           \\| |            |             /                                     2                                                /     /                                             2                           \\|      /                                     2                                                /     /                                             2                           \\|
|            |          4 /  /      2                           \                                           2     |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/||   4 /  /      2                           \                                           2     |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|| |            |          4 /  /      2                           \                                           2     |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/||   4 /  /      2                           \                                           2     |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/||
|            |          \/   \- 9*im (y) + (-40 + 9*re(y))*re(y)/  + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y))  *sin|--------------------------------------------------------------------------------||   \/   \- 9*im (y) + (-40 + 9*re(y))*re(y)/  + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y))  *cos|--------------------------------------------------------------------------------|| |            |          \/   \- 9*im (y) + (-40 + 9*re(y))*re(y)/  + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y))  *sin|--------------------------------------------------------------------------------||   \/   \- 9*im (y) + (-40 + 9*re(y))*re(y)/  + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y))  *cos|--------------------------------------------------------------------------------||
|3*re(y)     |3*im(y)                                                                                             \                                       2                                        /|                                                                                             \                                       2                                        /| |3*re(y)     |3*im(y)                                                                                             \                                       2                                        /|                                                                                             \                                       2                                        /|
|------- + I*|------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|------- + I*|------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\   4        \   4                                                                                           4                                                                                      /                                                                                        4                                                                                      / \   4        \   4                                                                                           4                                                                                      /                                                                                        4                                                                                      /

\left(i \left(- \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) - \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{re}{\left(y\right)}}{4}\right) \left(i \left(\frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) + \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{re}{\left(y\right)}}{4}\right)

5*re(y)   5*I*im(y)
------- + ---------
   2          2

\frac{5 \operatorname{re}{\left(y\right)}}{2} + \frac{5 i \operatorname{im}{\left(y\right)}}{2}

5*re(y)/2 + 5*i*im(y)/2

Respuesta rápida [src]

                 /              __________________________________________________________________________________                                                                                      \       __________________________________________________________________________________                                                                                      
                 |             /                                     2                                                /     /                                             2                           \\|      /                                     2                                                /     /                                             2                           \\
                 |          4 /  /      2                           \                                           2     |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/||   4 /  /      2                           \                                           2     |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|
                 |          \/   \- 9*im (y) + (-40 + 9*re(y))*re(y)/  + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y))  *sin|--------------------------------------------------------------------------------||   \/   \- 9*im (y) + (-40 + 9*re(y))*re(y)/  + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y))  *cos|--------------------------------------------------------------------------------|
     3*re(y)     |3*im(y)                                                                                             \                                       2                                        /|                                                                                             \                                       2                                        /
x1 = ------- + I*|------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
        4        \   4                                                                                           4                                                                                      /                                                                                        4

x_{1} = i \left(- \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) - \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{re}{\left(y\right)}}{4}

                 /              __________________________________________________________________________________                                                                                      \       __________________________________________________________________________________                                                                                      
                 |             /                                     2                                                /     /                                             2                           \\|      /                                     2                                                /     /                                             2                           \\
                 |          4 /  /      2                           \                                           2     |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/||   4 /  /      2                           \                                           2     |atan2\(-40 + 9*re(y))*im(y) + 9*im(y)*re(y), - 9*im (y) + (-40 + 9*re(y))*re(y)/|
                 |          \/   \- 9*im (y) + (-40 + 9*re(y))*re(y)/  + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y))  *sin|--------------------------------------------------------------------------------||   \/   \- 9*im (y) + (-40 + 9*re(y))*re(y)/  + ((-40 + 9*re(y))*im(y) + 9*im(y)*re(y))  *cos|--------------------------------------------------------------------------------|
     3*re(y)     |3*im(y)                                                                                             \                                       2                                        /|                                                                                             \                                       2                                        /
x2 = ------- + I*|------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
        4        \   4                                                                                           4                                                                                      /                                                                                        4

x_{2} = i \left(\frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{im}{\left(y\right)}}{4}\right) + \frac{\sqrt[4]{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{im}{\left(y\right)} + 9 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(9 \operatorname{re}{\left(y\right)} - 40\right) \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{4} + \frac{3 \operatorname{re}{\left(y\right)}}{4}

x2 = i*((((9*re(y) - 40)*re(y) - 9*im(y)^2)^2 + ((9*re(y) - 40)*im(y) + 9*re(y)*im(y))^2)^(1/4)*sin(atan2((9*re(y) - 40)*im(y) + 9*re(y)*im(y, (9*re(y) - 40)*re(y) - 9*im(y)^2)/2)/4 + 3*im(y)/4) + (((9*re(y) - 40)*re(y) - 9*im(y)^2)^2 + ((9*re(y) - 40)*im(y) + 9*re(y)*im(y))^2)^(1/4)*cos(atan2((9*re(y) - 40)*im(y) + 9*re(y)*im(y), (9*re(y) - 40)*re(y) - 9*im(y)^2)/2)/4 + 3*re(y)/4)

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

2*x^2-3*x*y+5*y=0 la ecuación

Solución numérica:

Solución

2x^2-3xy+5y=0 la ecuación