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- La ecuación:
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Ecuación (x-3)*(x+2)=0
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Ecuación z^2-6*z+10=0
-
Ecuación 4/(x-4)=-5
-
Ecuación (x-6)^2=-24*x
- Expresar {x} en función de y en la ecuación:
- -7*x-13*y=5
- 15*x+1*y=19
- 7*x-1*y=-7
- -14*x-12*y=5
-
Expresiones idénticas
- tg*π(2x− veintiuno)/ seis =√ tres / tres
- tg multiplicar por π(2x−21) dividir por 6 es igual a √3 dividir por 3
- tg multiplicar por π(2x− veintiuno) dividir por seis es igual a √ tres dividir por tres
- tgπ(2x−21)/6=√3/3
- tgπ2x−21/6=√3/3
- tg*π(2x−21) dividir por 6=√3 dividir por 3
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Expresiones con funciones
- tg
- tg(x)=-1/2
- tg(x)=-2
- tg(x)=-sqrt(3)/3
- tg(x)=3
- tg(x)=sqrt(3)/3
tg*π(2x−21)/6=√3/3 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
___
tan(p)*I*(2*x - 21) \/ 3
------------------- = -----
6 3
$$\frac{i \tan{\left(p \right)} \left(2 x - 21\right)}{6} = \frac{\sqrt{3}}{3}$$
Solución detallada
Tenemos la ecuación
$$\frac{i \tan{\left(p \right)} \left(2 x - 21\right)}{6} = \frac{\sqrt{3}}{3}$$
cambiamos
$$\frac{i \left(2 x - 21\right) \tan{\left(p \right)}}{6} - 1 - \frac{\sqrt{3}}{3} = 0$$
$$\frac{i \tan{\left(p \right)} \left(2 x - 21\right)}{6} - 1 - \frac{\sqrt{3}}{3} = 0$$
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:
$$\frac{i w \left(2 x - 21\right)}{6} - \frac{\sqrt{3}}{3} = 1$$
Dividamos ambos miembros de la ecuación en (-sqrt(3)/3 + i*w*(-21 + 2*x)/6)/w
Obtenemos la respuesta: w = -2*i*(3 + sqrt(3))/(-21 + 2*x)
hacemos cambio inverso
$$\tan{\left(p \right)} = w$$
sustituimos w:
$$\frac{i \tan{\left(p \right)} \left(2 x - 21\right)}{6} = \frac{\sqrt{3}}{3}$$
cambiamos
$$\frac{i \left(2 x - 21\right) \tan{\left(p \right)}}{6} - 1 - \frac{\sqrt{3}}{3} = 0$$
$$\frac{i \tan{\left(p \right)} \left(2 x - 21\right)}{6} - 1 - \frac{\sqrt{3}}{3} = 0$$
Sustituimos
$$w = \tan{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-1 - sqrt3/3 + i*w2*x/6+21/6 = 0
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-1 - sqrt(3)/3 + i*w*(-21 + 2*x)/6 = 0
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(2 x - 21\right)}{6} - \frac{\sqrt{3}}{3} = 1$$
Dividamos ambos miembros de la ecuación en (-sqrt(3)/3 + i*w*(-21 + 2*x)/6)/w
w = 1 / ((-sqrt(3)/3 + i*w*(-21 + 2*x)/6)/w)
Obtenemos la respuesta: w = -2*i*(3 + sqrt(3))/(-21 + 2*x)
hacemos cambio inverso
$$\tan{\left(p \right)} = w$$
sustituimos w:
Gráfica
Suma y producto de raíces
[src]
suma
___ ___
21 \/ 3 *sinh(2*im(p)) I*\/ 3 *sin(2*re(p))
-- - -------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------
2 / 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))) /
$$\frac{21}{2} - \frac{\sqrt{3} i \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{\sqrt{3} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)}$$
=
___ ___
21 \/ 3 *sinh(2*im(p)) I*\/ 3 *sin(2*re(p))
-- - -------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------
2 / 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))) /
$$\frac{21}{2} - \frac{\sqrt{3} i \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{\sqrt{3} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)}$$
producto
___ ___
21 \/ 3 *sinh(2*im(p)) I*\/ 3 *sin(2*re(p))
-- - -------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------
2 / 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))) /
$$\frac{21}{2} - \frac{\sqrt{3} i \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{\sqrt{3} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)}$$
=
/ / ___ ___ \\
-\-21*sin(2*re(p)) + I*\-21*sinh(2*im(p)) + 2*\/ 3 *cos(2*re(p)) + 2*\/ 3 *cosh(2*im(p))//
-------------------------------------------------------------------------------------------
2*sin(2*re(p)) + 2*I*sinh(2*im(p))
$$- \frac{i \left(2 \sqrt{3} \cos{\left(2 \operatorname{re}{\left(p\right)} \right)} - 21 \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)} + 2 \sqrt{3} \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right) - 21 \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{2 \sin{\left(2 \operatorname{re}{\left(p\right)} \right)} + 2 i \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}$$
-(-21*sin(2*re(p)) + i*(-21*sinh(2*im(p)) + 2*sqrt(3)*cos(2*re(p)) + 2*sqrt(3)*cosh(2*im(p))))/(2*sin(2*re(p)) + 2*i*sinh(2*im(p)))
Respuesta rápida
[src]
___ ___
21 \/ 3 *sinh(2*im(p)) I*\/ 3 *sin(2*re(p))
x1 = -- - -------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------
2 / 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))) /
$$x_{1} = \frac{21}{2} - \frac{\sqrt{3} i \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{\sqrt{3} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)}$$
x1 = 21/2 - 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))))