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- La ecuación:
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Ecuación x^4+2*x^2-8=0
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Ecuación 1/(x-3)^2-3/(x-3)-4=0
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Ecuación 9*(x-5)=-x
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Ecuación 13x+10=6x-4
- Expresar {x} en función de y en la ecuación:
- 7*x-6*y=-2
- 10*x-2*y=0
- 13*x-15*y=-6
- 4*x-7*y=4
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Expresiones idénticas
- sinП(ocho *x+ siete): cuatro =-sqrt(dos)/ dos
- seno de П(8 multiplicar por x más 7):4 es igual a menos raíz cuadrada de (2) dividir por 2
- seno de П(ocho multiplicar por x más siete): cuatro es igual a menos raíz cuadrada de (dos) dividir por dos
- sinП(8*x+7):4=-√(2)/2
- sinП(8x+7):4=-sqrt(2)/2
- sinП8x+7:4=-sqrt2/2
- sinП(8*x+7):4=-sqrt(2) dividir por 2
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Expresiones semejantes
- cos(x)+sqrt((2-sqrt(2))/2)*(sinx+1)=0
- sinx/4=-sqrt2/2
- cos(x)+sqrt((2-sqrt2)/2)*(sin(x)+1)=0
- -((sqrt(2)/2)*x-(sqrt(2)/2)*y)^2-4*((sqrt(2)/2)*x-(sqrt(2)/2)*y)*((sqrt(2)/2)*x+(sqrt(2)/2)*y)-((sqrt(2)/2)*x+(sqrt(2)/2)*y)^2+3=0
- sinП(8*x+7):4=+sqrt(2)/2
- sinП(8*x-7):4=-sqrt(2)/2
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(2*x+3)=x
- sqrt(-72+17*x)=x
- sqrt(6+x-x^2)=1-x
- sqrt(cos(x)-1)=0
- sqrt(x+3)=x+3
sinП(8*x+7):4=-sqrt(2)/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
___
sin(p)*I*(8*x + 7) -\/ 2
------------------ = -------
4 2
$$\frac{i \sin{\left(p \right)} \left(8 x + 7\right)}{4} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Solución detallada
Tenemos la ecuación
$$\frac{i \sin{\left(p \right)} \left(8 x + 7\right)}{4} = \frac{\left(-1\right) \sqrt{2}}{2}$$
cambiamos
$$\frac{i \left(8 x + 7\right) \sin{\left(p \right)}}{4} - 1 + \frac{\sqrt{2}}{2} = 0$$
$$\frac{i \sin{\left(p \right)} \left(8 x + 7\right)}{4} - 1 - \frac{\left(-1\right) \sqrt{2}}{2} = 0$$
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:
$$\frac{i w \left(8 x + 7\right)}{4} + \frac{\sqrt{2}}{2} = 1$$
Dividamos ambos miembros de la ecuación en (sqrt(2)/2 + i*w*(7 + 8*x)/4)/w
Obtenemos la respuesta: w = 2*i*(-2 + sqrt(2))/(7 + 8*x)
hacemos cambio inverso
$$\sin{\left(p \right)} = w$$
sustituimos w:
$$\frac{i \sin{\left(p \right)} \left(8 x + 7\right)}{4} = \frac{\left(-1\right) \sqrt{2}}{2}$$
cambiamos
$$\frac{i \left(8 x + 7\right) \sin{\left(p \right)}}{4} - 1 + \frac{\sqrt{2}}{2} = 0$$
$$\frac{i \sin{\left(p \right)} \left(8 x + 7\right)}{4} - 1 - \frac{\left(-1\right) \sqrt{2}}{2} = 0$$
Sustituimos
$$w = \sin{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-1 - -sqrt+2)/2 + i*w8*x/4+7/4 = 0
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-1 + sqrt(2)/2 + i*w*(7 + 8*x)/4 = 0
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(8 x + 7\right)}{4} + \frac{\sqrt{2}}{2} = 1$$
Dividamos ambos miembros de la ecuación en (sqrt(2)/2 + i*w*(7 + 8*x)/4)/w
w = 1 / ((sqrt(2)/2 + i*w*(7 + 8*x)/4)/w)
Obtenemos la respuesta: w = 2*i*(-2 + sqrt(2))/(7 + 8*x)
hacemos cambio inverso
$$\sin{\left(p \right)} = w$$
sustituimos w:
Gráfica
Suma y producto de raíces
[src]
suma
___ ___
7 \/ 2 *cos(re(p))*sinh(im(p)) I*\/ 2 *cosh(im(p))*sin(re(p))
- - + ------------------------------------------------------- + -------------------------------------------------------
8 / 2 2 2 2 \ / 2 2 2 2 \
4*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 4*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$- \frac{7}{8} + \frac{\sqrt{2} i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
=
___ ___
7 \/ 2 *cos(re(p))*sinh(im(p)) I*\/ 2 *cosh(im(p))*sin(re(p))
- - + ------------------------------------------------------- + -------------------------------------------------------
8 / 2 2 2 2 \ / 2 2 2 2 \
4*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 4*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$- \frac{7}{8} + \frac{\sqrt{2} i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
producto
___ ___
7 \/ 2 *cos(re(p))*sinh(im(p)) I*\/ 2 *cosh(im(p))*sin(re(p))
- - + ------------------------------------------------------- + -------------------------------------------------------
8 / 2 2 2 2 \ / 2 2 2 2 \
4*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 4*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$- \frac{7}{8} + \frac{\sqrt{2} i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
=
/ / ___ \ \
-\I*\- 2*\/ 2 + 7*cos(re(p))*sinh(im(p))/ + 7*cosh(im(p))*sin(re(p))/
-----------------------------------------------------------------------
8*cosh(im(p))*sin(re(p)) + 8*I*cos(re(p))*sinh(im(p))
$$- \frac{i \left(7 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} - 2 \sqrt{2}\right) + 7 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{8 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)} + 8 i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}$$
-(i*(-2*sqrt(2) + 7*cos(re(p))*sinh(im(p))) + 7*cosh(im(p))*sin(re(p)))/(8*cosh(im(p))*sin(re(p)) + 8*i*cos(re(p))*sinh(im(p)))
Respuesta rápida
[src]
___ ___
7 \/ 2 *cos(re(p))*sinh(im(p)) I*\/ 2 *cosh(im(p))*sin(re(p))
x1 = - - + ------------------------------------------------------- + -------------------------------------------------------
8 / 2 2 2 2 \ / 2 2 2 2 \
4*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 4*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$x_{1} = - \frac{7}{8} + \frac{\sqrt{2} i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{4 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
x1 = -7/8 + sqrt(2)*i*sin(re(p))*cosh(im(p))/(4*(sin(re(p))^2*cosh(im(p))^2 + cos(re(p))^2*sinh(im(p))^2)) + sqrt(2)*cos(re(p))*sinh(im(p))/(4*(sin(re(p))^2*cosh(im(p))^2 + cos(re(p))^2*sinh(im(p))^2))