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Expresiones idénticas
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Expresiones semejantes
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(x^2-6x)+(x2-6x)-56=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 x - 6*x + x2 - 6*x - 56 = 0
$$\left(\left(- 6 x + x_{2}\right) + \left(x^{2} - 6 x\right)\right) - 56 = 0$$
Solución detallada
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
$$a = 1$$
$$b = -12$$
$$c = x_{2} - 56$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{\sqrt{368 - 4 x_{2}}}{2} + 6$$
$$x_{2} = 6 - \frac{\sqrt{368 - 4 x_{2}}}{2}$$
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
$$a = 1$$
$$b = -12$$
$$c = x_{2} - 56$$
, entonces
D = b^2 - 4 * a * c =
(-12)^2 - 4 * (1) * (-56 + x2) = 368 - 4*x2
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{\sqrt{368 - 4 x_{2}}}{2} + 6$$
$$x_{2} = 6 - \frac{\sqrt{368 - 4 x_{2}}}{2}$$
Teorema de Cardano-Vieta
es ecuación cuadrática reducida
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -12$$
$$q = \frac{c}{a}$$
$$q = x_{2} - 56$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 12$$
$$x_{1} x_{2} = x_{2} - 56$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -12$$
$$q = \frac{c}{a}$$
$$q = x_{2} - 56$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 12$$
$$x_{1} x_{2} = x_{2} - 56$$
Gráfica
Respuesta rápida
[src]
__________________________ __________________________
4 / 2 2 /atan2(-im(x2), 92 - re(x2))\ 4 / 2 2 /atan2(-im(x2), 92 - re(x2))\
x1 = 6 - \/ (92 - re(x2)) + im (x2) *cos|---------------------------| - I*\/ (92 - re(x2)) + im (x2) *sin|---------------------------|
\ 2 / \ 2 /
$$x_{1} = - i \sqrt[4]{\left(92 - \operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},92 - \operatorname{re}{\left(x_{2}\right)} \right)}}{2} \right)} - \sqrt[4]{\left(92 - \operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},92 - \operatorname{re}{\left(x_{2}\right)} \right)}}{2} \right)} + 6$$
__________________________ __________________________
4 / 2 2 /atan2(-im(x2), 92 - re(x2))\ 4 / 2 2 /atan2(-im(x2), 92 - re(x2))\
x2 = 6 + \/ (92 - re(x2)) + im (x2) *cos|---------------------------| + I*\/ (92 - re(x2)) + im (x2) *sin|---------------------------|
\ 2 / \ 2 /
$$x_{2} = i \sqrt[4]{\left(92 - \operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},92 - \operatorname{re}{\left(x_{2}\right)} \right)}}{2} \right)} + \sqrt[4]{\left(92 - \operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},92 - \operatorname{re}{\left(x_{2}\right)} \right)}}{2} \right)} + 6$$
x2 = i*((92 - re(x2))^2 + im(x2)^2)^(1/4)*sin(atan2(-im(x2, 92 - re(x2))/2) + ((92 - re(x2))^2 + im(x2)^2)^(1/4)*cos(atan2(-im(x2), 92 - re(x2))/2) + 6)
Suma y producto de raíces
[src]
suma
__________________________ __________________________ __________________________ __________________________
4 / 2 2 /atan2(-im(x2), 92 - re(x2))\ 4 / 2 2 /atan2(-im(x2), 92 - re(x2))\ 4 / 2 2 /atan2(-im(x2), 92 - re(x2))\ 4 / 2 2 /atan2(-im(x2), 92 - re(x2))\
6 - \/ (92 - re(x2)) + im (x2) *cos|---------------------------| - I*\/ (92 - re(x2)) + im (x2) *sin|---------------------------| + 6 + \/ (92 - re(x2)) + im (x2) *cos|---------------------------| + I*\/ (92 - re(x2)) + im (x2) *sin|---------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(- i \sqrt[4]{\left(92 - \operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},92 - \operatorname{re}{\left(x_{2}\right)} \right)}}{2} \right)} - \sqrt[4]{\left(92 - \operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},92 - \operatorname{re}{\left(x_{2}\right)} \right)}}{2} \right)} + 6\right) + \left(i \sqrt[4]{\left(92 - \operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},92 - \operatorname{re}{\left(x_{2}\right)} \right)}}{2} \right)} + \sqrt[4]{\left(92 - \operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},92 - \operatorname{re}{\left(x_{2}\right)} \right)}}{2} \right)} + 6\right)$$
=
12
$$12$$
producto
/ __________________________ __________________________ \ / __________________________ __________________________ \ | 4 / 2 2 /atan2(-im(x2), 92 - re(x2))\ 4 / 2 2 /atan2(-im(x2), 92 - re(x2))\| | 4 / 2 2 /atan2(-im(x2), 92 - re(x2))\ 4 / 2 2 /atan2(-im(x2), 92 - re(x2))\| |6 - \/ (92 - re(x2)) + im (x2) *cos|---------------------------| - I*\/ (92 - re(x2)) + im (x2) *sin|---------------------------||*|6 + \/ (92 - re(x2)) + im (x2) *cos|---------------------------| + I*\/ (92 - re(x2)) + im (x2) *sin|---------------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(- i \sqrt[4]{\left(92 - \operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},92 - \operatorname{re}{\left(x_{2}\right)} \right)}}{2} \right)} - \sqrt[4]{\left(92 - \operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},92 - \operatorname{re}{\left(x_{2}\right)} \right)}}{2} \right)} + 6\right) \left(i \sqrt[4]{\left(92 - \operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},92 - \operatorname{re}{\left(x_{2}\right)} \right)}}{2} \right)} + \sqrt[4]{\left(92 - \operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x_{2}\right)},92 - \operatorname{re}{\left(x_{2}\right)} \right)}}{2} \right)} + 6\right)$$
=
-56 + I*im(x2) + re(x2)
$$\operatorname{re}{\left(x_{2}\right)} + i \operatorname{im}{\left(x_{2}\right)} - 56$$
-56 + i*im(x2) + re(x2)