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- La ecuación:
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Ecuación 3^x=7
- Ecuación x+y-4=0
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Ecuación z^2+z+1=0
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Ecuación 8*x=2
- Expresar {x} en función de y en la ecuación:
- -17*x-15*y=-17
- 12*x-20*y=10
- -20*x-13*y=15
- 7*x-6*y=-10
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Expresiones idénticas
- tgπ(5x- veintiocho)/ seis =√ tres / tres
- tgπ(5x menos 28) dividir por 6 es igual a √3 dividir por 3
- tgπ(5x menos veintiocho) dividir por seis es igual a √ tres dividir por tres
- tgπ5x-28/6=√3/3
- tgπ(5x-28) dividir por 6=√3 dividir por 3
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Expresiones semejantes
- tgπ(5x+28)/6=√3/3
tgπ(5x-28)/6=√3/3 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
___
tan(p)*I*(5*x - 28) \/ 3
------------------- = -----
6 3
$$\frac{i \tan{\left(p \right)} \left(5 x - 28\right)}{6} = \frac{\sqrt{3}}{3}$$
Solución detallada
Tenemos la ecuación
$$\frac{i \tan{\left(p \right)} \left(5 x - 28\right)}{6} = \frac{\sqrt{3}}{3}$$
cambiamos
$$\frac{i \left(5 x - 28\right) \tan{\left(p \right)}}{6} - 1 - \frac{\sqrt{3}}{3} = 0$$
$$\frac{i \tan{\left(p \right)} \left(5 x - 28\right)}{6} - 1 - \frac{\sqrt{3}}{3} = 0$$
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:
$$\frac{i w \left(5 x - 28\right)}{6} - \frac{\sqrt{3}}{3} = 1$$
Dividamos ambos miembros de la ecuación en (-sqrt(3)/3 + i*w*(-28 + 5*x)/6)/w
Obtenemos la respuesta: w = -2*i*(3 + sqrt(3))/(-28 + 5*x)
hacemos cambio inverso
$$\tan{\left(p \right)} = w$$
sustituimos w:
$$\frac{i \tan{\left(p \right)} \left(5 x - 28\right)}{6} = \frac{\sqrt{3}}{3}$$
cambiamos
$$\frac{i \left(5 x - 28\right) \tan{\left(p \right)}}{6} - 1 - \frac{\sqrt{3}}{3} = 0$$
$$\frac{i \tan{\left(p \right)} \left(5 x - 28\right)}{6} - 1 - \frac{\sqrt{3}}{3} = 0$$
Sustituimos
$$w = \tan{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-1 - sqrt3/3 + i*w5*x/6+28/6 = 0
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-1 - sqrt(3)/3 + i*w*(-28 + 5*x)/6 = 0
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(5 x - 28\right)}{6} - \frac{\sqrt{3}}{3} = 1$$
Dividamos ambos miembros de la ecuación en (-sqrt(3)/3 + i*w*(-28 + 5*x)/6)/w
w = 1 / ((-sqrt(3)/3 + i*w*(-28 + 5*x)/6)/w)
Obtenemos la respuesta: w = -2*i*(3 + sqrt(3))/(-28 + 5*x)
hacemos cambio inverso
$$\tan{\left(p \right)} = w$$
sustituimos w:
Gráfica
Suma y producto de raíces
[src]
suma
___ ___
28 2*\/ 3 *sinh(2*im(p)) 2*I*\/ 3 *sin(2*re(p))
-- - ---------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------
5 / 2 2 \ / 2 2 \
| sin (2*re(p)) sinh (2*im(p)) | | sin (2*re(p)) sinh (2*im(p)) |
5*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) 5*|------------------------------- + -------------------------------|*(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))) /
$$\frac{28}{5} - \frac{2 \sqrt{3} i \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{5 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{2 \sqrt{3} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{5 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)}$$
=
___ ___
28 2*\/ 3 *sinh(2*im(p)) 2*I*\/ 3 *sin(2*re(p))
-- - ---------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------
5 / 2 2 \ / 2 2 \
| sin (2*re(p)) sinh (2*im(p)) | | sin (2*re(p)) sinh (2*im(p)) |
5*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) 5*|------------------------------- + -------------------------------|*(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))) /
$$\frac{28}{5} - \frac{2 \sqrt{3} i \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{5 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{2 \sqrt{3} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{5 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)}$$
producto
___ ___
28 2*\/ 3 *sinh(2*im(p)) 2*I*\/ 3 *sin(2*re(p))
-- - ---------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------
5 / 2 2 \ / 2 2 \
| sin (2*re(p)) sinh (2*im(p)) | | sin (2*re(p)) sinh (2*im(p)) |
5*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) 5*|------------------------------- + -------------------------------|*(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))) /
$$\frac{28}{5} - \frac{2 \sqrt{3} i \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{5 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{2 \sqrt{3} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{5 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)}$$
=
/ / ___ ___ \\
-\-28*sin(2*re(p)) + 2*I*\-14*sinh(2*im(p)) + \/ 3 *cos(2*re(p)) + \/ 3 *cosh(2*im(p))//
-----------------------------------------------------------------------------------------
5*sin(2*re(p)) + 5*I*sinh(2*im(p))
$$- \frac{2 i \left(\sqrt{3} \cos{\left(2 \operatorname{re}{\left(p\right)} \right)} - 14 \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)} + \sqrt{3} \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right) - 28 \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{5 \sin{\left(2 \operatorname{re}{\left(p\right)} \right)} + 5 i \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}$$
-(-28*sin(2*re(p)) + 2*i*(-14*sinh(2*im(p)) + sqrt(3)*cos(2*re(p)) + sqrt(3)*cosh(2*im(p))))/(5*sin(2*re(p)) + 5*i*sinh(2*im(p)))
Respuesta rápida
[src]
___ ___
28 2*\/ 3 *sinh(2*im(p)) 2*I*\/ 3 *sin(2*re(p))
x1 = -- - ---------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------
5 / 2 2 \ / 2 2 \
| sin (2*re(p)) sinh (2*im(p)) | | sin (2*re(p)) sinh (2*im(p)) |
5*|------------------------------- + -------------------------------|*(cos(2*re(p)) + cosh(2*im(p))) 5*|------------------------------- + -------------------------------|*(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))) /
$$x_{1} = \frac{28}{5} - \frac{2 \sqrt{3} i \sin{\left(2 \operatorname{re}{\left(p\right)} \right)}}{5 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)} - \frac{2 \sqrt{3} \sinh{\left(2 \operatorname{im}{\left(p\right)} \right)}}{5 \left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(p\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(p\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(p\right)} \right)}\right)}$$
x1 = 28/5 - 2*sqrt(3)*i*sin(2*re(p))/(5*(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)))) - 2*sqrt(3)*sinh(2*im(p))/(5*(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))))