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- La ecuación:
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Ecuación x+9=0
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Ecuación 5*x^2+9*x=0
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Ecuación 3x^2=2x+x^3
- Expresar {x} en función de y en la ecuación:
- -6*x+11*y=-5
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- -14*x+4*y=-16
- 11*x-9*y=-4
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Expresiones idénticas
- cosπ(cuatro x+ setenta y dos)\4=− dos –√ dos .
- coseno de π(4x más 72)\4 es igual a −2–√2.
- coseno de π(cuatro x más setenta y dos)\4 es igual a − dos –√ dos .
- cosπ4x+72\4=−2–√2.
-
Expresiones semejantes
- cosπ(4x-72)\4=−2–√2.
cosπ(4x+72)\4=−2–√2. la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
cos(p)*I*(4*x + 72) ___
------------------- = -2 - \/ 2
4
$$\frac{i \cos{\left(p \right)} \left(4 x + 72\right)}{4} = -2 - \sqrt{2}$$
Solución detallada
Tenemos la ecuación
$$\frac{i \cos{\left(p \right)} \left(4 x + 72\right)}{4} = -2 - \sqrt{2}$$
cambiamos
$$i \left(x + 18\right) \cos{\left(p \right)} + 1 + \sqrt{2} = 0$$
$$\frac{i \cos{\left(p \right)} \left(4 x + 72\right)}{4} + 1 + \sqrt{2} = 0$$
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:
$$\frac{i w \left(4 x + 72\right)}{4} + \sqrt{2} = -1$$
Dividamos ambos miembros de la ecuación en (sqrt(2) + i*w*(72 + 4*x)/4)/w
Obtenemos la respuesta: w = i*(1 + sqrt(2))/(18 + x)
hacemos cambio inverso
$$\cos{\left(p \right)} = w$$
sustituimos w:
$$\frac{i \cos{\left(p \right)} \left(4 x + 72\right)}{4} = -2 - \sqrt{2}$$
cambiamos
$$i \left(x + 18\right) \cos{\left(p \right)} + 1 + \sqrt{2} = 0$$
$$\frac{i \cos{\left(p \right)} \left(4 x + 72\right)}{4} + 1 + \sqrt{2} = 0$$
Sustituimos
$$w = \cos{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
1 + sqrt2 + i*w4*x/4+72/4 = 0
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
1 + sqrt(2) + i*w*(72 + 4*x)/4 = 0
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(4 x + 72\right)}{4} + \sqrt{2} = -1$$
Dividamos ambos miembros de la ecuación en (sqrt(2) + i*w*(72 + 4*x)/4)/w
w = -1 / ((sqrt(2) + i*w*(72 + 4*x)/4)/w)
Obtenemos la respuesta: w = i*(1 + sqrt(2))/(18 + x)
hacemos cambio inverso
$$\cos{\left(p \right)} = w$$
sustituimos w:
Gráfica
Respuesta rápida
[src]
// ___ \ \ 2 2 / ___ \
|\2 + \/ 2 + 18*sin(re(p))*sinh(im(p))/*cos(re(p))*cosh(im(p)) 18*cos(re(p))*cosh(im(p))*sin(re(p))*sinh(im(p)) | 18*cos (re(p))*cosh (im(p)) \2 + \/ 2 + 18*sin(re(p))*sinh(im(p))/*sin(re(p))*sinh(im(p))
x1 = I*|-------------------------------------------------------------- - ---------------------------------------------------| - --------------------------------------------------- - --------------------------------------------------------------
| 2 2 2 2 2 2 2 2 | 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))/ cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$x_{1} = i \left(\frac{\left(18 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + \sqrt{2} + 2\right) \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{18 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}\right) - \frac{\left(18 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + \sqrt{2} + 2\right) \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{18 \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
x1 = i*((18*sin(re(p))*sinh(im(p)) + sqrt(2) + 2)*cos(re(p))*cosh(im(p))/(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2) - 18*sin(re(p))*cos(re(p))*sinh(im(p))*cosh(im(p))/(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2)) - (18*sin(re(p))*sinh(im(p)) + sqrt(2) + 2)*sin(re(p))*sinh(im(p))/(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2) - 18*cos(re(p))^2*cosh(im(p))^2/(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2)
Suma y producto de raíces
[src]
suma
// ___ \ \ 2 2 / ___ \ |\2 + \/ 2 + 18*sin(re(p))*sinh(im(p))/*cos(re(p))*cosh(im(p)) 18*cos(re(p))*cosh(im(p))*sin(re(p))*sinh(im(p)) | 18*cos (re(p))*cosh (im(p)) \2 + \/ 2 + 18*sin(re(p))*sinh(im(p))/*sin(re(p))*sinh(im(p)) I*|-------------------------------------------------------------- - ---------------------------------------------------| - --------------------------------------------------- - -------------------------------------------------------------- | 2 2 2 2 2 2 2 2 | 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))/ cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$i \left(\frac{\left(18 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + \sqrt{2} + 2\right) \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{18 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}\right) - \frac{\left(18 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + \sqrt{2} + 2\right) \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{18 \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
=
// ___ \ \ 2 2 / ___ \ |\2 + \/ 2 + 18*sin(re(p))*sinh(im(p))/*cos(re(p))*cosh(im(p)) 18*cos(re(p))*cosh(im(p))*sin(re(p))*sinh(im(p)) | 18*cos (re(p))*cosh (im(p)) \2 + \/ 2 + 18*sin(re(p))*sinh(im(p))/*sin(re(p))*sinh(im(p)) I*|-------------------------------------------------------------- - ---------------------------------------------------| - --------------------------------------------------- - -------------------------------------------------------------- | 2 2 2 2 2 2 2 2 | 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))/ cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$i \left(\frac{\left(18 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + \sqrt{2} + 2\right) \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{18 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}\right) - \frac{\left(18 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + \sqrt{2} + 2\right) \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{18 \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
producto
// ___ \ \ 2 2 / ___ \ |\2 + \/ 2 + 18*sin(re(p))*sinh(im(p))/*cos(re(p))*cosh(im(p)) 18*cos(re(p))*cosh(im(p))*sin(re(p))*sinh(im(p)) | 18*cos (re(p))*cosh (im(p)) \2 + \/ 2 + 18*sin(re(p))*sinh(im(p))/*sin(re(p))*sinh(im(p)) I*|-------------------------------------------------------------- - ---------------------------------------------------| - --------------------------------------------------- - -------------------------------------------------------------- | 2 2 2 2 2 2 2 2 | 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))/ cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$i \left(\frac{\left(18 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + \sqrt{2} + 2\right) \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{18 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}\right) - \frac{\left(18 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + \sqrt{2} + 2\right) \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{18 \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
=
/ / ___ \ \
-\I*\2 + \/ 2 + 18*sin(re(p))*sinh(im(p))/ - 18*cos(re(p))*cosh(im(p))/
-------------------------------------------------------------------------
-cos(re(p))*cosh(im(p)) + I*sin(re(p))*sinh(im(p))
$$- \frac{i \left(18 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + \sqrt{2} + 2\right) - 18 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} - \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}$$
-(i*(2 + sqrt(2) + 18*sin(re(p))*sinh(im(p))) - 18*cos(re(p))*cosh(im(p)))/(-cos(re(p))*cosh(im(p)) + i*sin(re(p))*sinh(im(p)))