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Otras calculadoras
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- La ecuación:
-
Ecuación x^4=(x-20)^2
-
Ecuación 5-2*(x-1)=4-x
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Ecuación (x+6)^3=25*(x+6)
- Ecuación x+y+2=0
- Expresar {x} en función de y en la ecuación:
- 10*x-18*y=3
- 16*x+7*y=8
- -19*x+1*y=0
- -11*x-15*y=14
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Expresiones idénticas
- cospi(x+ uno)/ cuatro =√ dos / dos
- coseno de número pi (x más 1) dividir por 4 es igual a √2 dividir por 2
- coseno de número pi (x más uno) dividir por cuatro es igual a √ dos dividir por dos
- cospix+1/4=√2/2
- cospi(x+1) dividir por 4=√2 dividir por 2
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Expresiones semejantes
- cos*pi*(x+1)/4=sqrt(2)/2
- cos(pi*(x+1)/4)=2^(1/2)/2
- cos(pi*(x+1)/4)=√2/2
- cos((pi*(x+1))/4)=sqrt(2)/2
- cospi(x-1)/4=√2/2
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Expresiones con funciones
- cospi
- cospi(4*x-6)/3=12
- cospi(4x-7)/6=sqrt(3)/2
- cospix=-2
- cospix=6
- cospi(2x+36)/4=-sqrt(2)/2
cospi(x+1)/4=√2/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
___
cos(p)*I*(x + 1) \/ 2
---------------- = -----
4 2
$$\frac{i \cos{\left(p \right)} \left(x + 1\right)}{4} = \frac{\sqrt{2}}{2}$$
Solución detallada
Tenemos la ecuación
$$\frac{i \cos{\left(p \right)} \left(x + 1\right)}{4} = \frac{\sqrt{2}}{2}$$
cambiamos
$$\frac{i \left(x + 1\right) \cos{\left(p \right)}}{4} - 1 - \frac{\sqrt{2}}{2} = 0$$
$$\frac{i \cos{\left(p \right)} \left(x + 1\right)}{4} - 1 - \frac{\sqrt{2}}{2} = 0$$
Sustituimos
$$w = \cos{\left(p \right)}$$
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:
$$\frac{i w \left(x + 1\right)}{4} - \frac{\sqrt{2}}{2} = 1$$
Dividamos ambos miembros de la ecuación en (-sqrt(2)/2 + i*w*(1 + x)/4)/w
Obtenemos la respuesta: w = -2*i*(2 + sqrt(2))/(1 + x)
hacemos cambio inverso
$$\cos{\left(p \right)} = w$$
sustituimos w:
$$\frac{i \cos{\left(p \right)} \left(x + 1\right)}{4} = \frac{\sqrt{2}}{2}$$
cambiamos
$$\frac{i \left(x + 1\right) \cos{\left(p \right)}}{4} - 1 - \frac{\sqrt{2}}{2} = 0$$
$$\frac{i \cos{\left(p \right)} \left(x + 1\right)}{4} - 1 - \frac{\sqrt{2}}{2} = 0$$
Sustituimos
$$w = \cos{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-1 - sqrt2/2 + i*wx/4+1/4 = 0
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-1 - sqrt(2)/2 + i*w*(1 + x)/4 = 0
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(x + 1\right)}{4} - \frac{\sqrt{2}}{2} = 1$$
Dividamos ambos miembros de la ecuación en (-sqrt(2)/2 + i*w*(1 + x)/4)/w
w = 1 / ((-sqrt(2)/2 + i*w*(1 + x)/4)/w)
Obtenemos la respuesta: w = -2*i*(2 + sqrt(2))/(1 + x)
hacemos cambio inverso
$$\cos{\left(p \right)} = w$$
sustituimos w:
Gráfica
Suma y producto de raíces
[src]
suma
___ ___
2*\/ 2 *sin(re(p))*sinh(im(p)) 2*I*\/ 2 *cos(re(p))*cosh(im(p))
-1 + --------------------------------------------------- - ---------------------------------------------------
2 2 2 2 2 2 2 2
cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$-1 + \frac{2 \sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{2 \sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
=
___ ___
2*\/ 2 *sin(re(p))*sinh(im(p)) 2*I*\/ 2 *cos(re(p))*cosh(im(p))
-1 + --------------------------------------------------- - ---------------------------------------------------
2 2 2 2 2 2 2 2
cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$-1 + \frac{2 \sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{2 \sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
producto
___ ___
2*\/ 2 *sin(re(p))*sinh(im(p)) 2*I*\/ 2 *cos(re(p))*cosh(im(p))
-1 + --------------------------------------------------- - ---------------------------------------------------
2 2 2 2 2 2 2 2
cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$-1 + \frac{2 \sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{2 \sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
=
/ / ___ \ \
-\I*\- 2*\/ 2 + sin(re(p))*sinh(im(p))/ - cos(re(p))*cosh(im(p))/
-------------------------------------------------------------------
-cos(re(p))*cosh(im(p)) + I*sin(re(p))*sinh(im(p))
$$- \frac{i \left(\sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} - 2 \sqrt{2}\right) - \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} - \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}$$
-(i*(-2*sqrt(2) + sin(re(p))*sinh(im(p))) - cos(re(p))*cosh(im(p)))/(-cos(re(p))*cosh(im(p)) + i*sin(re(p))*sinh(im(p)))
Respuesta rápida
[src]
___ ___
2*\/ 2 *sin(re(p))*sinh(im(p)) 2*I*\/ 2 *cos(re(p))*cosh(im(p))
x1 = -1 + --------------------------------------------------- - ---------------------------------------------------
2 2 2 2 2 2 2 2
cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$x_{1} = -1 + \frac{2 \sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{2 \sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
x1 = -1 + 2*sqrt(2)*sin(re(p))*sinh(im(p))/(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2) - 2*sqrt(2)*i*cos(re(p))*cosh(im(p))/(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2)