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La ecuación:
Ecuación x^4=(4x-21)^2
Ecuación (x+2)/9=(x-3)/2
Ecuación 1-2(5+3x)=15
Ecuación 2*x+2=-3
Expresar {x} en función de y en la ecuación:
-9*x-4*y=-20
12*x-14*y=20
5*x-13*y=17
-16*x+14*y=-9
Derivada de:
1/2
Integral de d{x}:
1/2
Suma de la serie:
1/2
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
Expresiones semejantes
sin((pi(5x+15))/6)=1/2
sinpi(5*x-15)/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}

Simplificar

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

-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)))

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Expresiones idénticas

Expresiones semejantes

sinpi(5*x+15)/6=1/2 la ecuación

Solución numérica:

Solución