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- La ecuación:
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Ecuación x^2=12
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Ecuación -27x+220=-5x
-
Ecuación x^2+5x=36
-
Ecuación 3*x=8
- Expresar {x} en función de y en la ecuación:
- -17*x+2*y=9
- 10*x-15*y=16
- -17*x+2*y=-4
- -2*x-19*y=3
- Suma de la serie:
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n^2
- Límite de la función:
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n^2
- Gráfico de la función y =:
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n^2
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Expresiones idénticas
- factorial(m)+ doce =n^ dos
- factorial(m) más 12 es igual a n al cuadrado
- factorial(m) más doce es igual a n en el grado dos
- factorial(m)+12=n2
- factorialm+12=n2
- factorial(m)+12=n²
- factorial(m)+12=n en el grado 2
- factorialm+12=n^2
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Expresiones semejantes
- factorial(m)-12=n^2
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Expresiones con funciones
- factorial
- factorial(77)=3^35
- factorial(2*x)/((6*factorial(2*x-3)))=14*factorial(x)/factorial(x-3)
- factorial(x-1)/(2*factorial(x-3))+factorial(x)/(6*factorial(x-3))=16
- factorial(5)+10*x=2
- factorial(x)/factorial(x-2)=56
factorial(m)+12=n^2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$m! + 12 = n^{2}$$
en
$$- n^{2} + \left(m! + 12\right) = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$n_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$n_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = -1$$
$$b = 0$$
$$c = m! + 12$$
, entonces
La ecuación tiene dos raíces.
o
$$n_{1} = - \frac{\sqrt{4 m! + 48}}{2}$$
$$n_{2} = \frac{\sqrt{4 m! + 48}}{2}$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$m! + 12 = n^{2}$$
en
$$- n^{2} + \left(m! + 12\right) = 0$$
Es la ecuación de la forma
a*n^2 + b*n + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$n_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$n_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = -1$$
$$b = 0$$
$$c = m! + 12$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-1) * (12 + factorial(m)) = 48 + 4*factorial(m)
La ecuación tiene dos raíces.
n1 = (-b + sqrt(D)) / (2*a)
n2 = (-b - sqrt(D)) / (2*a)
o
$$n_{1} = - \frac{\sqrt{4 m! + 48}}{2}$$
$$n_{2} = \frac{\sqrt{4 m! + 48}}{2}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$m! + 12 = n^{2}$$
de
$$a n^{2} + b n + c = 0$$
como ecuación cuadrática reducida
$$n^{2} + \frac{b n}{a} + \frac{c}{a} = 0$$
$$n^{2} - m! - 12 = 0$$
$$n^{2} + n p + q = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - m! - 12$$
Fórmulas de Cardano-Vieta
$$n_{1} + n_{2} = - p$$
$$n_{1} n_{2} = q$$
$$n_{1} + n_{2} = 0$$
$$n_{1} n_{2} = - m! - 12$$
$$m! + 12 = n^{2}$$
de
$$a n^{2} + b n + c = 0$$
como ecuación cuadrática reducida
$$n^{2} + \frac{b n}{a} + \frac{c}{a} = 0$$
$$n^{2} - m! - 12 = 0$$
$$n^{2} + n p + q = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - m! - 12$$
Fórmulas de Cardano-Vieta
$$n_{1} + n_{2} = - p$$
$$n_{1} n_{2} = q$$
$$n_{1} + n_{2} = 0$$
$$n_{1} n_{2} = - m! - 12$$
Gráfica
Respuesta rápida
[src]
______________________________________________ ______________________________________________
4 / 2 2 /atan2(im(Gamma(1 + m)), 12 + re(Gamma(1 + m)))\ 4 / 2 2 /atan2(im(Gamma(1 + m)), 12 + re(Gamma(1 + m)))\
n1 = - \/ (12 + re(Gamma(1 + m))) + im (Gamma(1 + m)) *cos|----------------------------------------------| - I*\/ (12 + re(Gamma(1 + m))) + im (Gamma(1 + m)) *sin|----------------------------------------------|
\ 2 / \ 2 /
$$n_{1} = - i \sqrt[4]{\left(\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12\right)^{2} + \left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)},\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12\right)^{2} + \left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)},\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12 \right)}}{2} \right)}$$
______________________________________________ ______________________________________________
4 / 2 2 /atan2(im(Gamma(1 + m)), 12 + re(Gamma(1 + m)))\ 4 / 2 2 /atan2(im(Gamma(1 + m)), 12 + re(Gamma(1 + m)))\
n2 = \/ (12 + re(Gamma(1 + m))) + im (Gamma(1 + m)) *cos|----------------------------------------------| + I*\/ (12 + re(Gamma(1 + m))) + im (Gamma(1 + m)) *sin|----------------------------------------------|
\ 2 / \ 2 /
$$n_{2} = i \sqrt[4]{\left(\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12\right)^{2} + \left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)},\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12\right)^{2} + \left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)},\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12 \right)}}{2} \right)}$$
n2 = i*((re(gamma(m + 1)) + 12)^2 + im(gamma(m + 1))^2)^(1/4)*sin(atan2(im(gamma(m + 1), re(gamma(m + 1)) + 12)/2) + ((re(gamma(m + 1)) + 12)^2 + im(gamma(m + 1))^2)^(1/4)*cos(atan2(im(gamma(m + 1)), re(gamma(m + 1)) + 12)/2))
Suma y producto de raíces
[src]
suma
______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________
4 / 2 2 /atan2(im(Gamma(1 + m)), 12 + re(Gamma(1 + m)))\ 4 / 2 2 /atan2(im(Gamma(1 + m)), 12 + re(Gamma(1 + m)))\ 4 / 2 2 /atan2(im(Gamma(1 + m)), 12 + re(Gamma(1 + m)))\ 4 / 2 2 /atan2(im(Gamma(1 + m)), 12 + re(Gamma(1 + m)))\
- \/ (12 + re(Gamma(1 + m))) + im (Gamma(1 + m)) *cos|----------------------------------------------| - I*\/ (12 + re(Gamma(1 + m))) + im (Gamma(1 + m)) *sin|----------------------------------------------| + \/ (12 + re(Gamma(1 + m))) + im (Gamma(1 + m)) *cos|----------------------------------------------| + I*\/ (12 + re(Gamma(1 + m))) + im (Gamma(1 + m)) *sin|----------------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(- i \sqrt[4]{\left(\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12\right)^{2} + \left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)},\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12\right)^{2} + \left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)},\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12 \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12\right)^{2} + \left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)},\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12\right)^{2} + \left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)},\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12 \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ ______________________________________________ ______________________________________________ \ / ______________________________________________ ______________________________________________ \ | 4 / 2 2 /atan2(im(Gamma(1 + m)), 12 + re(Gamma(1 + m)))\ 4 / 2 2 /atan2(im(Gamma(1 + m)), 12 + re(Gamma(1 + m)))\| |4 / 2 2 /atan2(im(Gamma(1 + m)), 12 + re(Gamma(1 + m)))\ 4 / 2 2 /atan2(im(Gamma(1 + m)), 12 + re(Gamma(1 + m)))\| |- \/ (12 + re(Gamma(1 + m))) + im (Gamma(1 + m)) *cos|----------------------------------------------| - I*\/ (12 + re(Gamma(1 + m))) + im (Gamma(1 + m)) *sin|----------------------------------------------||*|\/ (12 + re(Gamma(1 + m))) + im (Gamma(1 + m)) *cos|----------------------------------------------| + I*\/ (12 + re(Gamma(1 + m))) + im (Gamma(1 + m)) *sin|----------------------------------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(- i \sqrt[4]{\left(\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12\right)^{2} + \left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)},\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12\right)^{2} + \left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)},\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12 \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12\right)^{2} + \left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)},\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12\right)^{2} + \left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)},\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12 \right)}}{2} \right)}\right)$$
=
___________________________________________________________________ / 2 2 I*atan2(im(Gamma(1 + m)), 12 + re(Gamma(1 + m))) -\/ 144 + im (Gamma(1 + m)) + re (Gamma(1 + m)) + 24*re(Gamma(1 + m)) *e
$$- \sqrt{\left(\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)}\right)^{2} + 24 \operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + \left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)}\right)^{2} + 144} e^{i \operatorname{atan_{2}}{\left(\operatorname{im}{\left(\Gamma\left(m + 1\right)\right)},\operatorname{re}{\left(\Gamma\left(m + 1\right)\right)} + 12 \right)}}$$
-sqrt(144 + im(gamma(1 + m))^2 + re(gamma(1 + m))^2 + 24*re(gamma(1 + m)))*exp(i*atan2(im(gamma(1 + m)), 12 + re(gamma(1 + m))))