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