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La ecuación:
Ecuación x+(x/4)=-5
Ecuación z^4-81=0
Ecuación z^3=8
Ecuación x^3+x^2-2=0
Expresar {x} en función de y en la ecuación:
-18*x-8*y=-18
-13*x+12*y=-19
-1*x+11*y=-9
16*x-11*y=13
Expresiones idénticas
cuatro *cos(tres *x)^ dos - cuatro *cos(tres *x-pi/ dos)- uno = cero
4 multiplicar por coseno de (3 multiplicar por x) al cuadrado menos 4 multiplicar por coseno de (3 multiplicar por x menos número pi dividir por 2) menos 1 es igual a 0
cuatro multiplicar por coseno de (tres multiplicar por x) en el grado dos menos cuatro multiplicar por coseno de (tres multiplicar por x menos número pi dividir por dos) menos uno es igual a cero
4*cos(3*x)2-4*cos(3*x-pi/2)-1=0
4*cos3*x2-4*cos3*x-pi/2-1=0
4*cos(3*x)²-4*cos(3*x-pi/2)-1=0
4*cos(3*x) en el grado 2-4*cos(3*x-pi/2)-1=0
4cos(3x)^2-4cos(3x-pi/2)-1=0
4cos(3x)2-4cos(3x-pi/2)-1=0
4cos3x2-4cos3x-pi/2-1=0
4cos3x^2-4cos3x-pi/2-1=0
4*cos(3*x)^2-4*cos(3*x-pi/2)-1=O
4*cos(3*x)^2-4*cos(3*x-pi dividir por 2)-1=0
Expresiones semejantes
4*cos(3*x)^2-4*cos(3*x-pi/2)+1=0
4*cos(3*x)^2-4*cos(3*x+pi/2)-1=0
4*cos(3*x)^2+4*cos(3*x-pi/2)-1=0

4cos(3x)^2-4cos(3x-pi/2)-1=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

     2             /      pi\        
4*cos (3*x) - 4*cos|3*x - --| - 1 = 0
                   \      2 /

$$\left(4 \cos^{2}{\left(3 x \right)} - 4 \cos{\left(3 x - \frac{\pi}{2} \right)}\right) - 1 = 0$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

                  /    /        ___\\         /    /        ___\\         /    /        ___\\         /    /        ___\\
                  |    |2   I*\/ 5 ||         |    |2   I*\/ 5 ||         |    |2   I*\/ 5 ||         |    |2   I*\/ 5 ||
              2*re|atan|- - -------||   2*I*im|atan|- - -------||     2*re|atan|- + -------||   2*I*im|atan|- + -------||
pi   5*pi         \    \3      3   //         \    \3      3   //         \    \3      3   //         \    \3      3   //
-- + ---- + - ----------------------- - ------------------------- + - ----------------------- - -------------------------
18    18                 3                          3                            3                          3

$$\left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{2}{3} + \frac{\sqrt{5} i}{3} \right)}\right)}}{3} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{2}{3} + \frac{\sqrt{5} i}{3} \right)}\right)}}{3}\right) + \left(\left(\frac{\pi}{18} + \frac{5 \pi}{18}\right) + \left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{2}{3} - \frac{\sqrt{5} i}{3} \right)}\right)}}{3} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{2}{3} - \frac{\sqrt{5} i}{3} \right)}\right)}}{3}\right)\right)$$

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

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

producto

        /      /    /        ___\\         /    /        ___\\\ /      /    /        ___\\         /    /        ___\\\
        |      |    |2   I*\/ 5 ||         |    |2   I*\/ 5 ||| |      |    |2   I*\/ 5 ||         |    |2   I*\/ 5 |||
        |  2*re|atan|- - -------||   2*I*im|atan|- - -------||| |  2*re|atan|- + -------||   2*I*im|atan|- + -------|||
pi 5*pi |      \    \3      3   //         \    \3      3   //| |      \    \3      3   //         \    \3      3   //|
--*----*|- ----------------------- - -------------------------|*|- ----------------------- - -------------------------|
18  18  \             3                          3            / \             3                          3            /

$$\frac{\pi}{18} \frac{5 \pi}{18} \left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{2}{3} - \frac{\sqrt{5} i}{3} \right)}\right)}}{3} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{2}{3} - \frac{\sqrt{5} i}{3} \right)}\right)}}{3}\right) \left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{2}{3} + \frac{\sqrt{5} i}{3} \right)}\right)}}{3} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{2}{3} + \frac{\sqrt{5} i}{3} \right)}\right)}}{3}\right)$$

      /    /    /        ___\\     /    /        ___\\\ /    /    /        ___\\     /    /        ___\\\
    2 |    |    |2   I*\/ 5 ||     |    |2   I*\/ 5 ||| |    |    |2   I*\/ 5 ||     |    |2   I*\/ 5 |||
5*pi *|I*im|atan|- - -------|| + re|atan|- - -------|||*|I*im|atan|- + -------|| + re|atan|- + -------|||
      \    \    \3      3   //     \    \3      3   /// \    \    \3      3   //     \    \3      3   ///
---------------------------------------------------------------------------------------------------------
                                                   729

$$\frac{5 \pi^{2} \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{2}{3} - \frac{\sqrt{5} i}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{2}{3} - \frac{\sqrt{5} i}{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{2}{3} + \frac{\sqrt{5} i}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{2}{3} + \frac{\sqrt{5} i}{3} \right)}\right)}\right)}{729}$$

5*pi^2*(i*im(atan(2/3 - i*sqrt(5)/3)) + re(atan(2/3 - i*sqrt(5)/3)))*(i*im(atan(2/3 + i*sqrt(5)/3)) + re(atan(2/3 + i*sqrt(5)/3)))/729

Respuesta rápida [src]

     pi
x1 = --
     18

$$x_{1} = \frac{\pi}{18}$$

     5*pi
x2 = ----
      18

$$x_{2} = \frac{5 \pi}{18}$$

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

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

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

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

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

Respuesta numérica [src]

x1 = 90.2335223281068

x2 = 19.0240888467382

x3 = 88.1391272257137

x4 = 60.9119908946021

x5 = -17.9768912955416

x6 = -39.6189740202713

x7 = 2.26892802759263

x8 = 74.176493209759

x9 = -6.10865238198015

x10 = -50.0909495322373

x11 = 37.873644768277

x12 = 32.2885911618951

x13 = 39.9680398706701

x14 = 63.0063859969953

x15 = -64.0535835481919

x16 = 28.0998009571087

x17 = 4.36332312998582

x18 = 30.1941960595019

x19 = 86.0447321233204

x20 = -80.8087443673375

x21 = -41.7133691226645

x22 = 48.3456202802429

x23 = -418.006355852642

x24 = -85.6956662729216

x25 = -83.6012711705284

x26 = 10.6465084371654

x27 = -96.1676417848876

x28 = -24.9582083035189

x29 = 99.3092344384773

x30 = 55.3269372882203

x31 = -66.1479786505851

x32 = -36.8264472170804

x33 = -34.7320521146872

x34 = 69.9877030049726

x35 = -45.9021593274509

x36 = 83.9503370209273

x37 = 81.8559419185341

x38 = -87.7900613753148

x39 = 16.929693744345

x40 = 26.0054058547155

x41 = -43.8077642250577

x42 = -4.01425727958696

x43 = -13.7881010907552

x44 = -20.0712863979348

x45 = 65.7989128001862

x46 = -78.7143492649443

x47 = -99.6583002888762

x48 = 42.0624349730633

x49 = 95.120444233691

x50 = -94.0732466824944

x51 = -59.8647933434055

x52 = 78.3652834145454

x53 = -11.693705988362

x54 = 46.2512251778497

x55 = 0.872664625997165

x56 = -61.9591884457987

x57 = 76.2708883121522

x58 = -27.0526034059121

x59 = -57.7703982410123

x60 = 23.9110107523223

x61 = 0.174532925199433

x62 = 92.3279174305

x63 = -68.940505453776

x64 = -91.9788515801012

x65 = 9.25024503556995

x66 = -9.59931088596881

x67 = 44.1568300754565

x68 = -1.91986217719376

x69 = 56.7232006898157

x70 = 72.0820981073658

x71 = -71.0349005561692

x72 = -15.8824961931484

x73 = 53.2325421858271

x74 = 97.2148393360842

x75 = -47.9965544298441

x76 = -55.6760031386191

x77 = -89.884456477708

x78 = -53.5816080362259

x79 = 7.15584993317675

x80 = 67.8933079025794

x81 = 34.3829862642883

x81 = 34.3829862642883

Otras calculadoras

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Expresiones idénticas

Expresiones semejantes

4*cos(3*x)^2-4*cos(3*x-pi/2)-1=0 la ecuación

Solución numérica:

Solución

4cos(3x)^2-4cos(3x-pi/2)-1=0 la ecuación