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La ecuación:
Ecuación 3*x^2-x+2=0
Ecuación x^2=-74
Ecuación z^2+z+1=0
Ecuación 90+x-4*10=60
Expresar {x} en función de y en la ecuación:
5*x+19*y=-3
9*x+14*y=-10
-4*x-8*y=-20
-12*x-10*y=-16
Expresiones idénticas
cospi(dos x+ treinta y seis)/ cuatro =-sqrt(dos)/2
coseno de número pi (2x más 36) dividir por 4 es igual a menos raíz cuadrada de (2) dividir por 2
coseno de número pi (dos x más treinta y seis) dividir por cuatro es igual a menos raíz cuadrada de (dos) dividir por 2
cospi(2x+36)/4=-√(2)/2
cospi2x+36/4=-sqrt2/2
cospi(2x+36) dividir por 4=-sqrt(2) dividir por 2
Expresiones semejantes
cospi(2x-36)/4=-sqrt(2)/2
cospi(2x+36)/4=+sqrt(2)/2
Expresiones con funciones
Raíz cuadrada sqrt
sqrt(x-1)+3=x
sqrt(x-2)+sqrt(4-x)=sqrt(6-x)
sqrt(sqrt(3)cos(x)+sin(x)+2)=sin(3x)+1
sqrt(2x^2+21x-11)-sqrt(2x^2-9x+4)=sqrt(18*x-9)
sqrt(x^2-4)+sqrt(x^2-+x-2)=0

cospi(2x+36)/4=-sqrt(2)/2 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

                         ___ 
cos(p)*I*(2*x + 36)   -\/ 2  
------------------- = -------
         4               2

\frac{i \cos{\left(p \right)} \left(2 x + 36\right)}{4} = \frac{\left(-1\right) \sqrt{2}}{2}

Simplificar

Solución detallada

Tenemos la ecuación

\frac{i \cos{\left(p \right)} \left(2 x + 36\right)}{4} = \frac{\left(-1\right) \sqrt{2}}{2}

cambiamos

\frac{i \left(x + 18\right) \cos{\left(p \right)}}{2} - 1 + \frac{\sqrt{2}}{2} = 0

\frac{i \cos{\left(p \right)} \left(2 x + 36\right)}{4} - 1 - \frac{\left(-1\right) \sqrt{2}}{2} = 0

Sustituimos

w = \cos{\left(p \right)}

Abrimos los paréntesis en el miembro izquierdo de la ecuación

-1 - -sqrt+2)/2 + i*w2*x/4+36/4 = 0

Sumamos los términos semejantes en el miembro izquierdo de la ecuación:

-1 + sqrt(2)/2 + i*w*(36 + 2*x)/4 = 0

Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:

\frac{i w \left(2 x + 36\right)}{4} + \frac{\sqrt{2}}{2} = 1

Dividamos ambos miembros de la ecuación en (sqrt(2)/2 + i*w*(36 + 2*x)/4)/w

w = 1 / ((sqrt(2)/2 + i*w*(36 + 2*x)/4)/w)

Obtenemos la respuesta: w = i*(-2 + sqrt(2))/(18 + x)
hacemos cambio inverso

\cos{\left(p \right)} = w

sustituimos w:

Gráfica

Respuesta rápida [src]

                         ___                                                    ___                                 
                       \/ 2 *sin(re(p))*sinh(im(p))                         I*\/ 2 *cos(re(p))*cosh(im(p))          
x1 = -18 - --------------------------------------------------- + ---------------------------------------------------
              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} = -18 - \frac{\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{\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 = -18 - sqrt(2)*sin(re(p))*sinh(im(p))/(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^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)

Suma y producto de raíces [src]

suma

                    ___                                                    ___                                 
                  \/ 2 *sin(re(p))*sinh(im(p))                         I*\/ 2 *cos(re(p))*cosh(im(p))          
-18 - --------------------------------------------------- + ---------------------------------------------------
         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))

-18 - \frac{\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{\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 *sin(re(p))*sinh(im(p))                         I*\/ 2 *cos(re(p))*cosh(im(p))          
-18 - --------------------------------------------------- + ---------------------------------------------------
         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))

-18 - \frac{\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{\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 *sin(re(p))*sinh(im(p))                         I*\/ 2 *cos(re(p))*cosh(im(p))          
-18 - --------------------------------------------------- + ---------------------------------------------------
         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))

-18 - \frac{\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{\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  + 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}\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*(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)))

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Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

cospi(2x+36)/4=-sqrt(2)/2 la ecuación

Solución numérica:

Solución