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- La ecuación:
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Ecuación x^3-x^2-x-1=0
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Ecuación 3x-2(3x+4)=10
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Ecuación 12-4(x-3)=39-9x
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Ecuación 0,2x+2,7=1,4-1,1x
- Expresar {x} en función de y en la ecuación:
- -11*x-3*y=14
- 2*x-15*y=-1
- -18*x-6*y=-1
- 6*x+9*y=-9
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Expresiones idénticas
- tanpi(dos *x- dieciséis)/ seis =sqrt(tres)/ tres
- tangente de número pi (2 multiplicar por x menos 16) dividir por 6 es igual a raíz cuadrada de (3) dividir por 3
- tangente de número pi (dos multiplicar por x menos dieciséis) dividir por seis es igual a raíz cuadrada de (tres) dividir por tres
- tanpi(2*x-16)/6=√(3)/3
- tanpi(2x-16)/6=sqrt(3)/3
- tanpi2x-16/6=sqrt3/3
- tanpi(2*x-16) dividir por 6=sqrt(3) dividir por 3
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Expresiones semejantes
- tg(17x)=sqrt3/3
- tan(pi*x/6)=sqrt(3/3)
- tanpi(2*x+16)/6=sqrt(3)/3
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Expresiones con funciones
- tanpi
- tanpi*(x-3)/6=1
- Raíz cuadrada sqrt
- sqrt(12+x)-sqrt(1-x)=1
- sqrt(x-1)+3=x
- sqrt(x^2-4)=4-2x
- sqrt(x^2-x-3)=3
- sqrt-x=x+6
tanpi(2*x-16)/6=sqrt(3)/3 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
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tan(p)*I*(2*x - 16) \/ 3
------------------- = -----
6 3
$$\frac{i \tan{\left(p \right)} \left(2 x - 16\right)}{6} = \frac{\sqrt{3}}{3}$$
Solución detallada
Tenemos la ecuación
$$\frac{i \tan{\left(p \right)} \left(2 x - 16\right)}{6} = \frac{\sqrt{3}}{3}$$
cambiamos
$$\frac{i \left(x - 8\right) \tan{\left(p \right)}}{3} - 1 - \frac{\sqrt{3}}{3} = 0$$
$$\frac{i \tan{\left(p \right)} \left(2 x - 16\right)}{6} - 1 - \frac{\sqrt{3}}{3} = 0$$
Sustituimos
$$w = \tan{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(2 x - 16\right)}{6} - \frac{\sqrt{3}}{3} = 1$$
Dividamos ambos miembros de la ecuación en (-sqrt(3)/3 + i*w*(-16 + 2*x)/6)/w
Obtenemos la respuesta: w = -i*(3 + sqrt(3))/(-8 + x)
hacemos cambio inverso
$$\tan{\left(p \right)} = w$$
sustituimos w:
$$\frac{i \tan{\left(p \right)} \left(2 x - 16\right)}{6} = \frac{\sqrt{3}}{3}$$
cambiamos
$$\frac{i \left(x - 8\right) \tan{\left(p \right)}}{3} - 1 - \frac{\sqrt{3}}{3} = 0$$
$$\frac{i \tan{\left(p \right)} \left(2 x - 16\right)}{6} - 1 - \frac{\sqrt{3}}{3} = 0$$
Sustituimos
$$w = \tan{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-1 - sqrt3/3 + i*w2*x/6+16/6 = 0
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-1 - sqrt(3)/3 + i*w*(-16 + 2*x)/6 = 0
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(2 x - 16\right)}{6} - \frac{\sqrt{3}}{3} = 1$$
Dividamos ambos miembros de la ecuación en (-sqrt(3)/3 + i*w*(-16 + 2*x)/6)/w
w = 1 / ((-sqrt(3)/3 + i*w*(-16 + 2*x)/6)/w)
Obtenemos la respuesta: w = -i*(3 + sqrt(3))/(-8 + x)
hacemos cambio inverso
$$\tan{\left(p \right)} = w$$
sustituimos w:
Gráfica
Respuesta rápida
[src]
___ ___
\/ 3 *sinh(2*im(p)) I*\/ 3 *sin(2*re(p))
x1 = 8 - -------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------
/ 2 2 \ / 2 2 \
| sin (2*re(p)) sinh (2*im(p)) | | sin (2*re(p)) sinh (2*im(p)) |
|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) |------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p)))
| 2 2| | 2 2|
\(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) /
$$x_{1} = 8 - \frac{\sqrt{3} i \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{\sqrt{3} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)}$$
x1 = 8 - sqrt(3)*i*sin(2*re(p))/((sin(2*re(p))^2/(cos(2*re(p)) + cosh(2*im(p)))^2 + sinh(2*im(p))^2/(cos(2*re(p)) + cosh(2*im(p)))^2)*(cos(2*re(p)) + cosh(2*im(p)))) - sqrt(3)*sinh(2*im(p))/((sin(2*re(p))^2/(cos(2*re(p)) + cosh(2*im(p)))^2 + sinh(2*im(p))^2/(cos(2*re(p)) + cosh(2*im(p)))^2)*(cos(2*re(p)) + cosh(2*im(p))))
Suma y producto de raíces
[src]
suma
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\/ 3 *sinh(2*im(p)) I*\/ 3 *sin(2*re(p))
8 - -------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------
/ 2 2 \ / 2 2 \
| sin (2*re(p)) sinh (2*im(p)) | | sin (2*re(p)) sinh (2*im(p)) |
|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) |------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p)))
| 2 2| | 2 2|
\(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) /
$$8 - \frac{\sqrt{3} i \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{\sqrt{3} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)}$$
=
___ ___
\/ 3 *sinh(2*im(p)) I*\/ 3 *sin(2*re(p))
8 - -------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------
/ 2 2 \ / 2 2 \
| sin (2*re(p)) sinh (2*im(p)) | | sin (2*re(p)) sinh (2*im(p)) |
|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) |------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p)))
| 2 2| | 2 2|
\(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) /
$$8 - \frac{\sqrt{3} i \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{\sqrt{3} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)}$$
producto
___ ___
\/ 3 *sinh(2*im(p)) I*\/ 3 *sin(2*re(p))
8 - -------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------
/ 2 2 \ / 2 2 \
| sin (2*re(p)) sinh (2*im(p)) | | sin (2*re(p)) sinh (2*im(p)) |
|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) |------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p)))
| 2 2| | 2 2|
\(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) / \(cos(2*re(p)) + cosh(2*im(p))) (cos(2*re(p)) + cosh(2*im(p))) /
$$8 - \frac{\sqrt{3} i \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{\sqrt{3} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)}$$
=
/ / ___ ___ \\
-\-8*sin(2*re(p)) + I*\-8*sinh(2*im(p)) + \/ 3 *cos(2*re(p)) + \/ 3 *cosh(2*im(p))//
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I*sinh(2*im(p)) + sin(2*re(p))
$$- \frac{i \left(\sqrt{3} \cos{\left(2 \operatorname{re}{\left(p\right)} \right)} - 8 \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)} + \sqrt{3} \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right) - 8 \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\sin{\left(2 \operatorname{re}{\left(p\right)} \right)} + i \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}$$
-(-8*sin(2*re(p)) + i*(-8*sinh(2*im(p)) + sqrt(3)*cos(2*re(p)) + sqrt(3)*cosh(2*im(p))))/(i*sinh(2*im(p)) + sin(2*re(p)))