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La ecuación:
Ecuación (x+9)^2=36*x
Ecuación a+120=2000/5
Ecuación -x/11+x=50/11
Ecuación x^2+7x+6=0
Expresar {x} en función de y en la ecuación:
12*x+8*y=18
8*x+6*y=20
-2*x+18*y=13
-11*x-1*y=15
Expresiones idénticas
sqrt(tres)cos tres xcos(x-(dos pi/ tres))+2cos((pi/2)+(pi/3))= cero
raíz cuadrada de (3) coseno de 3x coseno de (x menos (2 número pi dividir por 3)) más 2 coseno de (( número pi dividir por 2) más ( número pi dividir por 3)) es igual a 0
raíz cuadrada de (tres) coseno de tres x coseno de (x menos (dos número pi dividir por tres)) más 2 coseno de (( número pi dividir por 2) más ( número pi dividir por 3)) es igual a cero
√(3)cos3xcos(x-(2pi/3))+2cos((pi/2)+(pi/3))=0
sqrt3cos3xcosx-2pi/3+2cospi/2+pi/3=0
sqrt(3)cos3xcos(x-(2pi/3))+2cos((pi/2)+(pi/3))=O
sqrt(3)cos3xcos(x-(2pi dividir por 3))+2cos((pi dividir por 2)+(pi dividir por 3))=0
Expresiones semejantes
sqrt(3)cos3xcos(x+(2pi/3))+2cos((pi/2)+(pi/3))=0
sqrt(3)cos3xcos(x-(2pi/3))-2cos((pi/2)+(pi/3))=0
sqrt(3)cos3xcos(x-(2pi/3))+2cos((pi/2)-(pi/3))=0
Expresiones con funciones
Raíz cuadrada sqrt
sqrt(1-x)=sqrt[3](x-2)
sqrt(x)^1=0
sqrt(x-2)+sqrt(x+6)=2
sqrt(x-2)+sqrt(4-x)=x^2-6*x+11
sqrt(x-a)+abs(x+a)=4

sqrt(3)cos3xcos(x-(2pi/3))+2cos((pi/2)+(pi/3))=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

  ___             /    2*pi\        /pi   pi\    
\/ 3 *cos(3*x)*cos|x - ----| + 2*cos|-- + --| = 0
                  \     3  /        \2    3 /

$$\sqrt{3} \cos{\left(3 x \right)} \cos{\left(x - \frac{2 \pi}{3} \right)} + 2 \cos{\left(\frac{\pi}{3} + \frac{\pi}{2} \right)} = 0$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

     -pi 
x1 = ----
      3

$$x_{1} = - \frac{\pi}{3}$$

     2*pi
x2 = ----
      3

$$x_{2} = \frac{2 \pi}{3}$$

                /     /        ___\         \
       5*pi     |  log\7 - 3*\/ 5 /   log(2)|
x3 = - ---- + I*|- ---------------- + ------|
        6       \         4             4   /

$$x_{3} = - \frac{5 \pi}{6} + i \left(\frac{\log{\left(2 \right)}}{4} - \frac{\log{\left(7 - 3 \sqrt{5} \right)}}{4}\right)$$

                /     /        ___\         \
       5*pi     |  log\7 + 3*\/ 5 /   log(2)|
x4 = - ---- + I*|- ---------------- + ------|
        6       \         4             4   /

$$x_{4} = - \frac{5 \pi}{6} + i \left(- \frac{\log{\left(3 \sqrt{5} + 7 \right)}}{4} + \frac{\log{\left(2 \right)}}{4}\right)$$

               /     4 ___      \
     pi        |     \/ 2       |
x5 = -- + I*log|----------------|
     6         |   _____________|
               |4 /         ___ |
               \\/  7 - 3*\/ 5  /

$$x_{5} = \frac{\pi}{6} + i \log{\left(\frac{\sqrt[4]{2}}{\sqrt[4]{7 - 3 \sqrt{5}}} \right)}$$

               /     4 ___      \
     pi        |     \/ 2       |
x6 = -- + I*log|----------------|
     6         |   _____________|
               |4 /         ___ |
               \\/  7 + 3*\/ 5  /

$$x_{6} = \frac{\pi}{6} + i \log{\left(\frac{\sqrt[4]{2}}{\sqrt[4]{3 \sqrt{5} + 7}} \right)}$$

x6 = pi/6 + i*log(2^(1/4)/(3*sqrt(5) + 7)^(1/4))

Suma y producto de raíces [src]

suma

                         /     /        ___\         \              /     /        ___\         \             /     4 ___      \             /     4 ___      \
  pi   2*pi     5*pi     |  log\7 - 3*\/ 5 /   log(2)|     5*pi     |  log\7 + 3*\/ 5 /   log(2)|   pi        |     \/ 2       |   pi        |     \/ 2       |
- -- + ---- + - ---- + I*|- ---------------- + ------| + - ---- + I*|- ---------------- + ------| + -- + I*log|----------------| + -- + I*log|----------------|
  3     3        6       \         4             4   /      6       \         4             4   /   6         |   _____________|   6         |   _____________|
                                                                                                              |4 /         ___ |             |4 /         ___ |
                                                                                                              \\/  7 - 3*\/ 5  /             \\/  7 + 3*\/ 5  /

$$\left(\frac{\pi}{6} + i \log{\left(\frac{\sqrt[4]{2}}{\sqrt[4]{3 \sqrt{5} + 7}} \right)}\right) + \left(\left(\left(- \frac{5 \pi}{6} + i \left(- \frac{\log{\left(3 \sqrt{5} + 7 \right)}}{4} + \frac{\log{\left(2 \right)}}{4}\right)\right) + \left(\left(- \frac{\pi}{3} + \frac{2 \pi}{3}\right) + \left(- \frac{5 \pi}{6} + i \left(\frac{\log{\left(2 \right)}}{4} - \frac{\log{\left(7 - 3 \sqrt{5} \right)}}{4}\right)\right)\right)\right) + \left(\frac{\pi}{6} + i \log{\left(\frac{\sqrt[4]{2}}{\sqrt[4]{7 - 3 \sqrt{5}}} \right)}\right)\right)$$

        /     /        ___\         \     /     /        ___\         \        /     4 ___      \        /     4 ___      \
        |  log\7 - 3*\/ 5 /   log(2)|     |  log\7 + 3*\/ 5 /   log(2)|        |     \/ 2       |        |     \/ 2       |
-pi + I*|- ---------------- + ------| + I*|- ---------------- + ------| + I*log|----------------| + I*log|----------------|
        \         4             4   /     \         4             4   /        |   _____________|        |   _____________|
                                                                               |4 /         ___ |        |4 /         ___ |
                                                                               \\/  7 - 3*\/ 5  /        \\/  7 + 3*\/ 5  /

$$- \pi + i \left(- \frac{\log{\left(3 \sqrt{5} + 7 \right)}}{4} + \frac{\log{\left(2 \right)}}{4}\right) + i \log{\left(\frac{\sqrt[4]{2}}{\sqrt[4]{3 \sqrt{5} + 7}} \right)} + i \left(\frac{\log{\left(2 \right)}}{4} - \frac{\log{\left(7 - 3 \sqrt{5} \right)}}{4}\right) + i \log{\left(\frac{\sqrt[4]{2}}{\sqrt[4]{7 - 3 \sqrt{5}}} \right)}$$

producto

          /           /     /        ___\         \\ /           /     /        ___\         \\ /          /     4 ___      \\ /          /     4 ___      \\
-pi  2*pi |  5*pi     |  log\7 - 3*\/ 5 /   log(2)|| |  5*pi     |  log\7 + 3*\/ 5 /   log(2)|| |pi        |     \/ 2       || |pi        |     \/ 2       ||
----*----*|- ---- + I*|- ---------------- + ------||*|- ---- + I*|- ---------------- + ------||*|-- + I*log|----------------||*|-- + I*log|----------------||
 3    3   \   6       \         4             4   // \   6       \         4             4   // |6         |   _____________|| |6         |   _____________||
                                                                                                |          |4 /         ___ || |          |4 /         ___ ||
                                                                                                \          \\/  7 - 3*\/ 5  // \          \\/  7 + 3*\/ 5  //

$$- \frac{\pi}{3} \frac{2 \pi}{3} \left(- \frac{5 \pi}{6} + i \left(\frac{\log{\left(2 \right)}}{4} - \frac{\log{\left(7 - 3 \sqrt{5} \right)}}{4}\right)\right) \left(- \frac{5 \pi}{6} + i \left(- \frac{\log{\left(3 \sqrt{5} + 7 \right)}}{4} + \frac{\log{\left(2 \right)}}{4}\right)\right) \left(\frac{\pi}{6} + i \log{\left(\frac{\sqrt[4]{2}}{\sqrt[4]{7 - 3 \sqrt{5}}} \right)}\right) \left(\frac{\pi}{6} + i \log{\left(\frac{\sqrt[4]{2}}{\sqrt[4]{3 \sqrt{5} + 7}} \right)}\right)$$

     /         /             /        ___\\\ /         /     /        ___\         \\                                                                                        
   2 |     3*I*\-log(2) + log\7 - 3*\/ 5 //| |     3*I*\- log\7 + 3*\/ 5 / + log(2)/| /            /     /        ___\         \\ /            /             /        ___\\\ 
-pi *|pi - --------------------------------|*|pi + ---------------------------------|*\10*pi - 3*I*\- log\7 + 3*\/ 5 / + log(2)//*\10*pi + 3*I*\-log(2) + log\7 - 3*\/ 5 /// 
     \                    2                / \                     2                /                                                                                        
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                    23328

$$- \frac{\pi^{2} \left(\pi - \frac{3 i \left(\log{\left(7 - 3 \sqrt{5} \right)} - \log{\left(2 \right)}\right)}{2}\right) \left(\pi + \frac{3 i \left(- \log{\left(3 \sqrt{5} + 7 \right)} + \log{\left(2 \right)}\right)}{2}\right) \left(10 \pi + 3 i \left(\log{\left(7 - 3 \sqrt{5} \right)} - \log{\left(2 \right)}\right)\right) \left(10 \pi - 3 i \left(- \log{\left(3 \sqrt{5} + 7 \right)} + \log{\left(2 \right)}\right)\right)}{23328}$$

-pi^2*(pi - 3*i*(-log(2) + log(7 - 3*sqrt(5)))/2)*(pi + 3*i*(-log(7 + 3*sqrt(5)) + log(2))/2)*(10*pi - 3*i*(-log(7 + 3*sqrt(5)) + log(2)))*(10*pi + 3*i*(-log(2) + log(7 - 3*sqrt(5))))/23328

Respuesta numérica [src]

x1 = -63.8790502707956

x2 = -76.4454211286131

x3 = -57.5958654013554

x4 = -151.843644922534

x5 = -54.4542725592394

x6 = -79.5870139801118

x7 = 74.3510260738122

x8 = 90.058989260729

x9 = 39.7935070648556

x10 = 14.6607655940305

x11 = 46.0766919949492

x12 = 58.6430627399819

x13 = -32.4631239907387

x14 = -51.3126799823713

x15 = 55.5014702713311

x16 = -85.8701991879186

x17 = -7.33038297821255

x18 = -51.3126801209398

x19 = -19.8967537467974

x20 = 17.8023586459812

x21 = -95.2949772607979

x22 = 77.4926188327457

x23 = -70.1622358253571

x24 = 8.37758033566263

x25 = -92.1533844039012

x26 = 17.8023584871419

x27 = 33.5103217080076

x28 = 11.5191731430674

x29 = -48268.4767272301

x30 = 74.3510261498103

x31 = 80.6342113135979

x32 = 96.3421746534546

x33 = 36.6519141667786

x34 = 30.3687289149186

x35 = -48.1710872469832

x36 = -35.604716822474

x37 = -29.3215315498923

x38 = 61.7846556424059

x39 = 83.7758042197919

x40 = 174.881990926498

x41 = 14.6607655249006

x42 = -73.3038286912739

x43 = 99.4837673918999

x44 = -101.578162588816

x45 = -10.471975423248

x46 = 68.067840627589

x47 = -4.18879009073537

x48 = -76.4454214215621

x49 = -13.613568243468

x50 = 52.3598774943011

x51 = 222.005880855276

x52 = -98.4365696987464

x53 = -26.1799388285815

x54 = -26.1799386687767

x55 = -4.18879016070987

x56 = -10.4719755682352

x57 = -48.171087170912

x57 = -48.171087170912

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Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

sqrt(3)cos3xcos(x-(2pi/3))+2cos((pi/2)+(pi/3))=0 la ecuación

Solución numérica:

Solución