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La ecuación:
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
Ecuación x^2+4=5x
Ecuación x(x^2+2x+1)=6(x+1)
Ecuación 4x+1=-3x+15
Expresar {x} en función de y en la ecuación:
-6*x-20*y=8
13*x-12*y=19
-9*x+11*y=9
-4*x-8*y=-20
Expresiones idénticas
(dos cos(x/ dos)-√(dos))*(sin(5x)+2)= cero
(2 coseno de (x dividir por 2) menos √(2)) multiplicar por ( seno de (5x) más 2) es igual a 0
(dos coseno de (x dividir por dos) menos √(dos)) multiplicar por ( seno de (5x) más 2) es igual a cero
(2cos(x/2)-√(2))(sin(5x)+2)=0
2cosx/2-√2sin5x+2=0
(2cos(x/2)-√(2))*(sin(5x)+2)=O
(2cos(x dividir por 2)-√(2))*(sin(5x)+2)=0
Expresiones semejantes
(2cos(x/2)-√(2))*(sin(5x)-2)=0
(2cos(x/2)+√(2))*(sin(5x)+2)=0
Expresiones con funciones
Seno sin
sin(x)=pi
sin(4*x)=0
sin(x)^2=1
sin(x)=(1/2)
sin(x)=0,5

(2cos(x/2)-√(2))*(sin(5x)+2)=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

/     /x\     ___\                   
|2*cos|-| - \/ 2 |*(sin(5*x) + 2) = 0
\     \2/        /

$$\left(\sin{\left(5 x \right)} + 2\right) \left(2 \cos{\left(\frac{x}{2} \right)} - \sqrt{2}\right) = 0$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

            /   ___________\
            |  /       ___ |
            |\/  2 - \/ 2  |
x1 = -4*atan|--------------|
            |   ___________|
            |  /       ___ |
            \\/  2 + \/ 2  /

$$x_{1} = - 4 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}$$

           /   ___________\
           |  /       ___ |
           |\/  2 - \/ 2  |
x2 = 4*atan|--------------|
           |   ___________|
           |  /       ___ |
           \\/  2 + \/ 2  /

$$x_{2} = 4 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}$$

           /    /        ___\\         /    /        ___\\
           |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||
       2*re|atan|- - -------||   2*I*im|atan|- - -------||
           \    \2      2   //         \    \2      2   //
x3 = - ----------------------- - -------------------------
                  5                          5

$$x_{3} = - \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5}$$

           /    /        ___\\         /    /        ___\\
           |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||
       2*re|atan|- + -------||   2*I*im|atan|- + -------||
           \    \2      2   //         \    \2      2   //
x4 = - ----------------------- - -------------------------
                  5                          5

$$x_{4} = - \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5}$$

x4 = -2*re(atan(1/2 + sqrt(3)*i/2))/5 - 2*i*im(atan(1/2 + sqrt(3)*i/2))/5

Suma y producto de raíces [src]

suma

                                                          /    /        ___\\         /    /        ___\\         /    /        ___\\         /    /        ___\\
        /   ___________\         /   ___________\         |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||
        |  /       ___ |         |  /       ___ |     2*re|atan|- - -------||   2*I*im|atan|- - -------||     2*re|atan|- + -------||   2*I*im|atan|- + -------||
        |\/  2 - \/ 2  |         |\/  2 - \/ 2  |         \    \2      2   //         \    \2      2   //         \    \2      2   //         \    \2      2   //
- 4*atan|--------------| + 4*atan|--------------| + - ----------------------- - ------------------------- + - ----------------------- - -------------------------
        |   ___________|         |   ___________|                5                          5                            5                          5            
        |  /       ___ |         |  /       ___ |                                                                                                                
        \\/  2 + \/ 2  /         \\/  2 + \/ 2  /

$$\left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5}\right) + \left(\left(- 4 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)} + 4 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}\right) + \left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5}\right)\right)$$

      /    /        ___\\       /    /        ___\\         /    /        ___\\         /    /        ___\\
      |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||
  2*re|atan|- + -------||   2*re|atan|- - -------||   2*I*im|atan|- + -------||   2*I*im|atan|- - -------||
      \    \2      2   //       \    \2      2   //         \    \2      2   //         \    \2      2   //
- ----------------------- - ----------------------- - ------------------------- - -------------------------
             5                         5                          5                           5

$$- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5}$$

producto

                                               /      /    /        ___\\         /    /        ___\\\ /      /    /        ___\\         /    /        ___\\\
       /   ___________\       /   ___________\ |      |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||| |      |    |1   I*\/ 3 ||         |    |1   I*\/ 3 |||
       |  /       ___ |       |  /       ___ | |  2*re|atan|- - -------||   2*I*im|atan|- - -------||| |  2*re|atan|- + -------||   2*I*im|atan|- + -------|||
       |\/  2 - \/ 2  |       |\/  2 - \/ 2  | |      \    \2      2   //         \    \2      2   //| |      \    \2      2   //         \    \2      2   //|
-4*atan|--------------|*4*atan|--------------|*|- ----------------------- - -------------------------|*|- ----------------------- - -------------------------|
       |   ___________|       |   ___________| \             5                          5            / \             5                          5            /
       |  /       ___ |       |  /       ___ |                                                                                                                
       \\/  2 + \/ 2  /       \\/  2 + \/ 2  /

$$- 4 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)} 4 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)} \left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5}\right) \left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5}\right)$$

         /   ___________\                                                                                                    
         |  /       ___ | /    /    /        ___\\     /    /        ___\\\ /    /    /        ___\\     /    /        ___\\\
        2|\/  2 - \/ 2  | |    |    |1   I*\/ 3 ||     |    |1   I*\/ 3 ||| |    |    |1   I*\/ 3 ||     |    |1   I*\/ 3 |||
-64*atan |--------------|*|I*im|atan|- + -------|| + re|atan|- + -------|||*|I*im|atan|- - -------|| + re|atan|- - -------|||
         |   ___________| \    \    \2      2   //     \    \2      2   /// \    \    \2      2   //     \    \2      2   ///
         |  /       ___ |                                                                                                    
         \\/  2 + \/ 2  /                                                                                                    
-----------------------------------------------------------------------------------------------------------------------------
                                                              25

$$- \frac{64 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right) \operatorname{atan}^{2}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}}{25}$$

-64*atan(sqrt(2 - sqrt(2))/sqrt(2 + sqrt(2)))^2*(i*im(atan(1/2 + i*sqrt(3)/2)) + re(atan(1/2 + i*sqrt(3)/2)))*(i*im(atan(1/2 - i*sqrt(3)/2)) + re(atan(1/2 - i*sqrt(3)/2)))/25

Respuesta numérica [src]

x1 = -86.3937979737193

x2 = 23.5619449019235

x3 = -98.9601685880785

x4 = -39.2699081698724

x5 = 98.9601685880785

x6 = -82198.2009848501

x7 = 86.3937979737193

x8 = 26.7035375555132

x9 = -48.6946861306418

x10 = -89.5353906273091

x11 = 48.6946861306418

x12 = -64.4026493985908

x13 = 14.1371669411541

x14 = -26.7035375555132

x15 = 39.2699081698724

x16 = 73.8274273593601

x17 = 89.5353906273091

x18 = 76.9690200129499

x19 = -23.5619449019235

x20 = 11458.9592039688

x21 = 64.4026493985908

x22 = -36.1283155162826

x23 = -1.5707963267949

x24 = 111.526539202438

x25 = -10.9955742875643

x26 = 1.5707963267949

x27 = -73.8274273593601

x28 = -177.499984927823

x29 = -76.9690200129499

x30 = -916199.944325986

x31 = 36.1283155162826

x32 = 61.261056745001

x33 = -61.261056745001

x34 = 10.9955742875643

x35 = -51.8362787842316

x36 = 51.8362787842316

x37 = 102.101761241668

x38 = -14.1371669411541

x38 = -14.1371669411541

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

(2cos(x/2)-√(2))*(sin(5x)+2)=0 la ecuación

Solución numérica:

Solución