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- La ecuación:
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Ecuación x^2-6x+9=0
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Ecuación (x-11)^4=(x+3)^4
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Ecuación √(x^2-1)^3=2*x
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Ecuación -x/12+x=55/12
- Expresar {x} en función de y en la ecuación:
- 18*x-11*y=2
- 12*x-14*y=20
- -3*x-20*y=-13
- -16*x+14*y=-9
- Derivada de:
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1/2
- Suma de la serie:
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1/2
- Límite de la función:
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1/2
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Expresiones idénticas
- sinpi(cinco *x+ quince)/ seis = uno / dos
- seno de número pi (5 multiplicar por x más 15) dividir por 6 es igual a 1 dividir por 2
- seno de número pi (cinco multiplicar por x más quince) dividir por seis es igual a uno dividir por dos
- sinpi(5x+15)/6=1/2
- sinpi5x+15/6=1/2
- sinpi(5*x+15) dividir por 6=1 dividir por 2
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Expresiones semejantes
- sinpi(5*x-15)/6=1/2
- sin((pi(5x+15))/6)=1/2
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Expresiones con funciones
- sinpi
- sinpi((x+11)/6)=-1/2
sinpi(5*x+15)/6=1/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
sin(p)*I*(5*x + 15)
------------------- = 1/2
6
$$\frac{i \sin{\left(p \right)} \left(5 x + 15\right)}{6} = \frac{1}{2}$$
Solución detallada
Tenemos la ecuación
$$\frac{i \sin{\left(p \right)} \left(5 x + 15\right)}{6} = \frac{1}{2}$$
cambiamos
$$\frac{5 i \left(x + 3\right) \sin{\left(p \right)}}{6} - \frac{3}{2} = 0$$
$$\frac{i \sin{\left(p \right)} \left(5 x + 15\right)}{6} - \frac{3}{2} = 0$$
Sustituimos
$$w = \sin{\left(p \right)}$$
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:
$$\frac{i w \left(5 x + 15\right)}{6} = \frac{3}{2}$$
Dividamos ambos miembros de la ecuación en i*(15 + 5*x)/6
Obtenemos la respuesta: w = -9*i/(15 + 5*x)
hacemos cambio inverso
$$\sin{\left(p \right)} = w$$
sustituimos w:
$$\frac{i \sin{\left(p \right)} \left(5 x + 15\right)}{6} = \frac{1}{2}$$
cambiamos
$$\frac{5 i \left(x + 3\right) \sin{\left(p \right)}}{6} - \frac{3}{2} = 0$$
$$\frac{i \sin{\left(p \right)} \left(5 x + 15\right)}{6} - \frac{3}{2} = 0$$
Sustituimos
$$w = \sin{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-3/2 + i*w5*x/6+15/6 = 0
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-3/2 + i*w*(15 + 5*x)/6 = 0
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(5 x + 15\right)}{6} = \frac{3}{2}$$
Dividamos ambos miembros de la ecuación en i*(15 + 5*x)/6
w = 3/2 / (i*(15 + 5*x)/6)
Obtenemos la respuesta: w = -9*i/(15 + 5*x)
hacemos cambio inverso
$$\sin{\left(p \right)} = w$$
sustituimos w:
Gráfica
Respuesta rápida
[src]
3*cos(re(p))*sinh(im(p)) 3*I*cosh(im(p))*sin(re(p))
x1 = -3 - ------------------------------------------------------- - -------------------------------------------------------
/ 2 2 2 2 \ / 2 2 2 2 \
5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$x_{1} = -3 - \frac{3 i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} - \frac{3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
x1 = -3 - 3*i*sin(re(p))*cosh(im(p))/(5*(sin(re(p))^2*cosh(im(p))^2 + cos(re(p))^2*sinh(im(p))^2)) - 3*cos(re(p))*sinh(im(p))/(5*(sin(re(p))^2*cosh(im(p))^2 + cos(re(p))^2*sinh(im(p))^2))
Suma y producto de raíces
[src]
suma
3*cos(re(p))*sinh(im(p)) 3*I*cosh(im(p))*sin(re(p))
-3 - ------------------------------------------------------- - -------------------------------------------------------
/ 2 2 2 2 \ / 2 2 2 2 \
5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$-3 - \frac{3 i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} - \frac{3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
=
3*cos(re(p))*sinh(im(p)) 3*I*cosh(im(p))*sin(re(p))
-3 - ------------------------------------------------------- - -------------------------------------------------------
/ 2 2 2 2 \ / 2 2 2 2 \
5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$-3 - \frac{3 i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} - \frac{3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
producto
3*cos(re(p))*sinh(im(p)) 3*I*cosh(im(p))*sin(re(p))
-3 - ------------------------------------------------------- - -------------------------------------------------------
/ 2 2 2 2 \ / 2 2 2 2 \
5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$-3 - \frac{3 i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} - \frac{3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
=
-(I*(3/5 + 3*cos(re(p))*sinh(im(p))) + 3*cosh(im(p))*sin(re(p)))
-----------------------------------------------------------------
cosh(im(p))*sin(re(p)) + I*cos(re(p))*sinh(im(p))
$$- \frac{i \left(3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + \frac{3}{5}\right) + 3 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)} + i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}$$
-(i*(3/5 + 3*cos(re(p))*sinh(im(p))) + 3*cosh(im(p))*sin(re(p)))/(cosh(im(p))*sin(re(p)) + i*cos(re(p))*sinh(im(p)))