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Expresiones idénticas
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Expresiones semejantes
- (4+x)(x+5)+x2=0
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- (4-x)(x-5)+x2=0
(4-x)(x+5)+x2=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Abramos la expresión en la ecuación
$$x_{2} + \left(4 - x\right) \left(x + 5\right) = 0$$
Obtenemos la ecuación cuadrática
$$- x^{2} - x + x_{2} + 20 = 0$$
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
$$a = -1$$
$$b = -1$$
$$c = x_{2} + 20$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = - \frac{\sqrt{4 x_{2} + 81}}{2} - \frac{1}{2}$$
$$x_{2} = \frac{\sqrt{4 x_{2} + 81}}{2} - \frac{1}{2}$$
$$x_{2} + \left(4 - x\right) \left(x + 5\right) = 0$$
Obtenemos la ecuación cuadrática
$$- x^{2} - x + x_{2} + 20 = 0$$
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
$$a = -1$$
$$b = -1$$
$$c = x_{2} + 20$$
, entonces
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (-1) * (20 + x2) = 81 + 4*x2
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = - \frac{\sqrt{4 x_{2} + 81}}{2} - \frac{1}{2}$$
$$x_{2} = \frac{\sqrt{4 x_{2} + 81}}{2} - \frac{1}{2}$$
Gráfica
Suma y producto de raíces
[src]
suma
_______________________________ _______________________________ _______________________________ _______________________________
4 / 2 2 /atan2(4*im(x2), 81 + 4*re(x2))\ 4 / 2 2 /atan2(4*im(x2), 81 + 4*re(x2))\ 4 / 2 2 /atan2(4*im(x2), 81 + 4*re(x2))\ 4 / 2 2 /atan2(4*im(x2), 81 + 4*re(x2))\
\/ (81 + 4*re(x2)) + 16*im (x2) *cos|------------------------------| I*\/ (81 + 4*re(x2)) + 16*im (x2) *sin|------------------------------| \/ (81 + 4*re(x2)) + 16*im (x2) *cos|------------------------------| I*\/ (81 + 4*re(x2)) + 16*im (x2) *sin|------------------------------|
1 \ 2 / \ 2 / 1 \ 2 / \ 2 /
- - - ---------------------------------------------------------------------- - ------------------------------------------------------------------------ + - - + ---------------------------------------------------------------------- + ------------------------------------------------------------------------
2 2 2 2 2 2
$$\left(- \frac{i \sqrt[4]{\left(4 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 16 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(x_{2}\right)},4 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{2} - \frac{\sqrt[4]{\left(4 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 16 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(x_{2}\right)},4 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{2} - \frac{1}{2}\right) + \left(\frac{i \sqrt[4]{\left(4 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 16 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(x_{2}\right)},4 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{2} + \frac{\sqrt[4]{\left(4 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 16 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(x_{2}\right)},4 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{2} - \frac{1}{2}\right)$$
=
-1
$$-1$$
producto
/ _______________________________ _______________________________ \ / _______________________________ _______________________________ \ | 4 / 2 2 /atan2(4*im(x2), 81 + 4*re(x2))\ 4 / 2 2 /atan2(4*im(x2), 81 + 4*re(x2))\| | 4 / 2 2 /atan2(4*im(x2), 81 + 4*re(x2))\ 4 / 2 2 /atan2(4*im(x2), 81 + 4*re(x2))\| | \/ (81 + 4*re(x2)) + 16*im (x2) *cos|------------------------------| I*\/ (81 + 4*re(x2)) + 16*im (x2) *sin|------------------------------|| | \/ (81 + 4*re(x2)) + 16*im (x2) *cos|------------------------------| I*\/ (81 + 4*re(x2)) + 16*im (x2) *sin|------------------------------|| | 1 \ 2 / \ 2 /| | 1 \ 2 / \ 2 /| |- - - ---------------------------------------------------------------------- - ------------------------------------------------------------------------|*|- - + ---------------------------------------------------------------------- + ------------------------------------------------------------------------| \ 2 2 2 / \ 2 2 2 /
$$\left(- \frac{i \sqrt[4]{\left(4 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 16 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(x_{2}\right)},4 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{2} - \frac{\sqrt[4]{\left(4 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 16 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(x_{2}\right)},4 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{2} - \frac{1}{2}\right) \left(\frac{i \sqrt[4]{\left(4 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 16 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(x_{2}\right)},4 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{2} + \frac{\sqrt[4]{\left(4 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 16 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(x_{2}\right)},4 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{2} - \frac{1}{2}\right)$$
=
-20 - re(x2) - I*im(x2)
$$- \operatorname{re}{\left(x_{2}\right)} - i \operatorname{im}{\left(x_{2}\right)} - 20$$
-20 - re(x2) - i*im(x2)
Respuesta rápida
[src]
_______________________________ _______________________________
4 / 2 2 /atan2(4*im(x2), 81 + 4*re(x2))\ 4 / 2 2 /atan2(4*im(x2), 81 + 4*re(x2))\
\/ (81 + 4*re(x2)) + 16*im (x2) *cos|------------------------------| I*\/ (81 + 4*re(x2)) + 16*im (x2) *sin|------------------------------|
1 \ 2 / \ 2 /
x1 = - - - ---------------------------------------------------------------------- - ------------------------------------------------------------------------
2 2 2
$$x_{1} = - \frac{i \sqrt[4]{\left(4 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 16 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(x_{2}\right)},4 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{2} - \frac{\sqrt[4]{\left(4 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 16 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(x_{2}\right)},4 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{2} - \frac{1}{2}$$
_______________________________ _______________________________
4 / 2 2 /atan2(4*im(x2), 81 + 4*re(x2))\ 4 / 2 2 /atan2(4*im(x2), 81 + 4*re(x2))\
\/ (81 + 4*re(x2)) + 16*im (x2) *cos|------------------------------| I*\/ (81 + 4*re(x2)) + 16*im (x2) *sin|------------------------------|
1 \ 2 / \ 2 /
x2 = - - + ---------------------------------------------------------------------- + ------------------------------------------------------------------------
2 2 2
$$x_{2} = \frac{i \sqrt[4]{\left(4 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 16 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(x_{2}\right)},4 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{2} + \frac{\sqrt[4]{\left(4 \operatorname{re}{\left(x_{2}\right)} + 81\right)^{2} + 16 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(4 \operatorname{im}{\left(x_{2}\right)},4 \operatorname{re}{\left(x_{2}\right)} + 81 \right)}}{2} \right)}}{2} - \frac{1}{2}$$
x2 = i*((4*re(x2) + 81)^2 + 16*im(x2)^2)^(1/4)*sin(atan2(4*im(x2, 4*re(x2) + 81)/2)/2 + ((4*re(x2) + 81)^2 + 16*im(x2)^2)^(1/4)*cos(atan2(4*im(x2), 4*re(x2) + 81)/2)/2 - 1/2)