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- La ecuación:
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Ecuación (x+9)^2=36*x
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Ecuación a+120=2000/5
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Ecuación -x/11+x=50/11
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Ecuación x^2+7x+6=0
- Expresar {x} en función de y en la ecuación:
- 12*x+8*y=18
- 8*x+6*y=20
- -2*x+18*y=13
- -11*x-1*y=15
- Forma canónica:
- (x^2-y^3)^2
-
Expresiones idénticas
- (x^ dos -y^ tres)^ dos
- (x al cuadrado menos y al cubo ) al cuadrado
- (x en el grado dos menos y en el grado tres) en el grado dos
- (x2-y3)2
- x2-y32
- (x²-y³)²
- (x en el grado 2-y en el grado 3) en el grado 2
- x^2-y^3^2
-
Expresiones semejantes
- (x^2+y^3)^2
(x^2-y^3)^2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
$$\left(x^{2} - y^{3}\right)^{2} = 0$$
cambiamos
$$x^{2} - y^{3} = 0$$
Es la ecuación de la forma
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
$$a = 1$$
$$b = 0$$
$$c = - y^{3}$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \sqrt{y^{3}}$$
$$x_{2} = - \sqrt{y^{3}}$$
cambiamos
$$x^{2} - y^{3} = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = - y^{3}$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-y^3) = 4*y^3
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \sqrt{y^{3}}$$
$$x_{2} = - \sqrt{y^{3}}$$
Gráfica
Respuesta rápida
[src]
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/ 2 2 / / 3 2 3 2 \\ / 2 2 / / 3 2 3 2 \\
4 / / 3 2 \ / 3 2 \ |atan2\- im (y) + 3*re (y)*im(y), re (y) - 3*im (y)*re(y)/| 4 / / 3 2 \ / 3 2 \ |atan2\- im (y) + 3*re (y)*im(y), re (y) - 3*im (y)*re(y)/|
x1 = - \/ \re (y) - 3*im (y)*re(y)/ + \- im (y) + 3*re (y)*im(y)/ *cos|---------------------------------------------------------| - I*\/ \re (y) - 3*im (y)*re(y)/ + \- im (y) + 3*re (y)*im(y)/ *sin|---------------------------------------------------------|
\ 2 / \ 2 /
$$x_{1} = - i \sqrt[4]{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3},\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3},\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}$$
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/ 2 2 / / 3 2 3 2 \\ / 2 2 / / 3 2 3 2 \\
4 / / 3 2 \ / 3 2 \ |atan2\- im (y) + 3*re (y)*im(y), re (y) - 3*im (y)*re(y)/| 4 / / 3 2 \ / 3 2 \ |atan2\- im (y) + 3*re (y)*im(y), re (y) - 3*im (y)*re(y)/|
x2 = \/ \re (y) - 3*im (y)*re(y)/ + \- im (y) + 3*re (y)*im(y)/ *cos|---------------------------------------------------------| + I*\/ \re (y) - 3*im (y)*re(y)/ + \- im (y) + 3*re (y)*im(y)/ *sin|---------------------------------------------------------|
\ 2 / \ 2 /
$$x_{2} = i \sqrt[4]{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3},\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3},\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}$$
x2 = i*((3*re(y)^2*im(y) - im(y)^3)^2 + (re(y)^3 - 3*re(y)*im(y)^2)^2)^(1/4)*sin(atan2(3*re(y)^2*im(y) - im(y^3, re(y)^3 - 3*re(y)*im(y)^2)/2) + ((3*re(y)^2*im(y) - im(y)^3)^2 + (re(y)^3 - 3*re(y)*im(y)^2)^2)^(1/4)*cos(atan2(3*re(y)^2*im(y) - im(y)^3, re(y)^3 - 3*re(y)*im(y)^2)/2))
Suma y producto de raíces
[src]
suma
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/ 2 2 / / 3 2 3 2 \\ / 2 2 / / 3 2 3 2 \\ / 2 2 / / 3 2 3 2 \\ / 2 2 / / 3 2 3 2 \\
4 / / 3 2 \ / 3 2 \ |atan2\- im (y) + 3*re (y)*im(y), re (y) - 3*im (y)*re(y)/| 4 / / 3 2 \ / 3 2 \ |atan2\- im (y) + 3*re (y)*im(y), re (y) - 3*im (y)*re(y)/| 4 / / 3 2 \ / 3 2 \ |atan2\- im (y) + 3*re (y)*im(y), re (y) - 3*im (y)*re(y)/| 4 / / 3 2 \ / 3 2 \ |atan2\- im (y) + 3*re (y)*im(y), re (y) - 3*im (y)*re(y)/|
- \/ \re (y) - 3*im (y)*re(y)/ + \- im (y) + 3*re (y)*im(y)/ *cos|---------------------------------------------------------| - I*\/ \re (y) - 3*im (y)*re(y)/ + \- im (y) + 3*re (y)*im(y)/ *sin|---------------------------------------------------------| + \/ \re (y) - 3*im (y)*re(y)/ + \- im (y) + 3*re (y)*im(y)/ *cos|---------------------------------------------------------| + I*\/ \re (y) - 3*im (y)*re(y)/ + \- im (y) + 3*re (y)*im(y)/ *sin|---------------------------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(- i \sqrt[4]{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3},\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3},\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3},\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3},\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ ___________________________________________________________ ___________________________________________________________ \ / ___________________________________________________________ ___________________________________________________________ \ | / 2 2 / / 3 2 3 2 \\ / 2 2 / / 3 2 3 2 \\| | / 2 2 / / 3 2 3 2 \\ / 2 2 / / 3 2 3 2 \\| | 4 / / 3 2 \ / 3 2 \ |atan2\- im (y) + 3*re (y)*im(y), re (y) - 3*im (y)*re(y)/| 4 / / 3 2 \ / 3 2 \ |atan2\- im (y) + 3*re (y)*im(y), re (y) - 3*im (y)*re(y)/|| |4 / / 3 2 \ / 3 2 \ |atan2\- im (y) + 3*re (y)*im(y), re (y) - 3*im (y)*re(y)/| 4 / / 3 2 \ / 3 2 \ |atan2\- im (y) + 3*re (y)*im(y), re (y) - 3*im (y)*re(y)/|| |- \/ \re (y) - 3*im (y)*re(y)/ + \- im (y) + 3*re (y)*im(y)/ *cos|---------------------------------------------------------| - I*\/ \re (y) - 3*im (y)*re(y)/ + \- im (y) + 3*re (y)*im(y)/ *sin|---------------------------------------------------------||*|\/ \re (y) - 3*im (y)*re(y)/ + \- im (y) + 3*re (y)*im(y)/ *cos|---------------------------------------------------------| + I*\/ \re (y) - 3*im (y)*re(y)/ + \- im (y) + 3*re (y)*im(y)/ *sin|---------------------------------------------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(- i \sqrt[4]{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3},\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3},\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3},\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3},\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}\right)$$
=
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/ 2 2 / 3 2 3 2 \
/ / 2 2 \ 2 / 2 2 \ 2 I*atan2\- im (y) + 3*re (y)*im(y), re (y) - 3*im (y)*re(y)/
-\/ \re (y) - 3*im (y)/ *re (y) + \- im (y) + 3*re (y)/ *im (y) *e
$$- \sqrt{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{3},\left(\operatorname{re}{\left(y\right)}\right)^{3} - 3 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}$$
-sqrt((re(y)^2 - 3*im(y)^2)^2*re(y)^2 + (-im(y)^2 + 3*re(y)^2)^2*im(y)^2)*exp(i*atan2(-im(y)^3 + 3*re(y)^2*im(y), re(y)^3 - 3*im(y)^2*re(y)))