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La ecuación:
Ecuación 6*x^2+x-7=0
Ecuación z^5+32=0
Ecuación 2-5(3+2x)=17
Ecuación (6*x+8)/2+5=5*x/3
Expresar {x} en función de y en la ecuación:
-9*x-12*y=-19
-8*x+3*y=-4
10*x+3*y=2
16*x-17*y=-15
Expresiones idénticas
4cos4x-3cos2x- uno = cero
4 coseno de 4x menos 3 coseno de 2x menos 1 es igual a 0
4 coseno de 4x menos 3 coseno de 2x menos uno es igual a cero
4cos4x-3cos2x-1=O
Expresiones semejantes
4cos4x-3cos2x+1=0
4cos4x+3cos2x-1=0

4cos4x-3cos2x-1=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

4*cos(4*x) - 3*cos(2*x) - 1 = 0

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

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

              /   /    /  ____\\\                                                                     /   /    /  ____\\\                                                                        
              |   |    |\/ 39 |||                                                                     |   |    |\/ 39 |||                                                                        
              |   |atan|------|||                                                                     |   |atan|------|||                                                                        
              |   |    \  5   /||                                                                     |   |    \  5   /||                                                                        
              |cos|------------||                                                                     |cos|------------||     /     /         ____\         \     /     /         ____\         \
              |   \     2      /|     /log(8)      /    ___\\           /log(8)      /    ___\\       |   \     2      /|   I*\- log\-5 - I*\/ 39 / + log(8)/   I*\- log\-5 + I*\/ 39 / + log(8)/
pi + pi - atan|-----------------| + I*|------ - log\2*\/ 2 /| + -pi + I*|------ - log\2*\/ 2 /| + atan|-----------------| + --------------------------------- + ---------------------------------
              |   /    /  ____\\|     \  2                  /           \  2                  /       |   /    /  ____\\|                   2                                   2                
              |   |    |\/ 39 |||                                                                     |   |    |\/ 39 |||                                                                        
              |   |atan|------|||                                                                     |   |atan|------|||                                                                        
              |   |    \  5   /||                                                                     |   |    \  5   /||                                                                        
              |sin|------------||                                                                     |sin|------------||                                                                        
              \   \     2      //                                                                     \   \     2      //

$$\left(\left(\left(\pi + \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{39}}{5} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{39}}{5} \right)}}{2} \right)}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)\right) + \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{39}}{5} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{39}}{5} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)\right) + \frac{i \left(\log{\left(8 \right)} - \log{\left(-5 - \sqrt{39} i \right)}\right)}{2}\right) + \frac{i \left(\log{\left(8 \right)} - \log{\left(-5 + \sqrt{39} i \right)}\right)}{2}$$

       /     /         ____\         \     /     /         ____\         \                              
     I*\- log\-5 + I*\/ 39 / + log(8)/   I*\- log\-5 - I*\/ 39 / + log(8)/       /log(8)      /    ___\\
pi + --------------------------------- + --------------------------------- + 2*I*|------ - log\2*\/ 2 /|
                     2                                   2                       \  2                  /

$$\pi + 2 i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right) + \frac{i \left(\log{\left(8 \right)} - \log{\left(-5 - \sqrt{39} i \right)}\right)}{2} + \frac{i \left(\log{\left(8 \right)} - \log{\left(-5 + \sqrt{39} i \right)}\right)}{2}$$

producto

     /         /   /    /  ____\\\                            \ /                                      /   /    /  ____\\\\                                                                    
     |         |   |    |\/ 39 |||                            | |                                      |   |    |\/ 39 ||||                                                                    
     |         |   |atan|------|||                            | |                                      |   |atan|------||||                                                                    
     |         |   |    \  5   /||                            | |                                      |   |    \  5   /|||                                                                    
     |         |cos|------------||                            | |                                      |cos|------------|||   /     /         ____\         \   /     /         ____\         \
     |         |   \     2      /|     /log(8)      /    ___\\| |        /log(8)      /    ___\\       |   \     2      /|| I*\- log\-5 - I*\/ 39 / + log(8)/ I*\- log\-5 + I*\/ 39 / + log(8)/
0*pi*|pi - atan|-----------------| + I*|------ - log\2*\/ 2 /||*|-pi + I*|------ - log\2*\/ 2 /| + atan|-----------------||*---------------------------------*---------------------------------
     |         |   /    /  ____\\|     \  2                  /| |        \  2                  /       |   /    /  ____\\||                 2                                 2                
     |         |   |    |\/ 39 |||                            | |                                      |   |    |\/ 39 ||||                                                                    
     |         |   |atan|------|||                            | |                                      |   |atan|------||||                                                                    
     |         |   |    \  5   /||                            | |                                      |   |    \  5   /|||                                                                    
     |         |sin|------------||                            | |                                      |sin|------------|||                                                                    
     \         \   \     2      //                            / \                                      \   \     2      ///

$$\frac{i \left(\log{\left(8 \right)} - \log{\left(-5 + \sqrt{39} i \right)}\right)}{2} \frac{i \left(\log{\left(8 \right)} - \log{\left(-5 - \sqrt{39} i \right)}\right)}{2} \cdot 0 \pi \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{39}}{5} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{39}}{5} \right)}}{2} \right)}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(- \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{39}}{5} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{39}}{5} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)$$

$$0$$

Respuesta rápida [src]

x1 = 0

$$x_{1} = 0$$

x2 = pi

$$x_{2} = \pi$$

              /   /    /  ____\\\                            
              |   |    |\/ 39 |||                            
              |   |atan|------|||                            
              |   |    \  5   /||                            
              |cos|------------||                            
              |   \     2      /|     /log(8)      /    ___\\
x3 = pi - atan|-----------------| + I*|------ - log\2*\/ 2 /|
              |   /    /  ____\\|     \  2                  /
              |   |    |\/ 39 |||                            
              |   |atan|------|||                            
              |   |    \  5   /||                            
              |sin|------------||                            
              \   \     2      //

$$x_{3} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{39}}{5} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{39}}{5} \right)}}{2} \right)}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)$$

                                           /   /    /  ____\\\
                                           |   |    |\/ 39 |||
                                           |   |atan|------|||
                                           |   |    \  5   /||
                                           |cos|------------||
             /log(8)      /    ___\\       |   \     2      /|
x4 = -pi + I*|------ - log\2*\/ 2 /| + atan|-----------------|
             \  2                  /       |   /    /  ____\\|
                                           |   |    |\/ 39 |||
                                           |   |atan|------|||
                                           |   |    \  5   /||
                                           |sin|------------||
                                           \   \     2      //

$$x_{4} = - \pi + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{39}}{5} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{39}}{5} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)$$

       /     /         ____\         \
     I*\- log\-5 - I*\/ 39 / + log(8)/
x5 = ---------------------------------
                     2

$$x_{5} = \frac{i \left(\log{\left(8 \right)} - \log{\left(-5 - \sqrt{39} i \right)}\right)}{2}$$

       /     /         ____\         \
     I*\- log\-5 + I*\/ 39 / + log(8)/
x6 = ---------------------------------
                     2

$$x_{6} = \frac{i \left(\log{\left(8 \right)} - \log{\left(-5 + \sqrt{39} i \right)}\right)}{2}$$

x6 = i*(log(8) - log(-5 + sqrt(39)*i))/2

Respuesta numérica [src]

x1 = 50.2654824463902

x2 = -43.9822971747869

x3 = -31.4159266269897

x4 = -75.3982237055582

x5 = 89.983223024238

x6 = -28.2743337718018

x7 = 8.30181403090342

x8 = -9.4247780560793

x9 = -17.7265919916728

x10 = -65.9734457654867

x11 = -35.6804831193537

x12 = 46.0009258739809

x13 = -63.9548170016618

x14 = 26.2557051585843

x15 = 43.9822971692295

x16 = 2.01862872372383

x17 = 59.6902604546743

x18 = 63.9548170016618

x19 = -12.5663705304908

x20 = -79.6627802696108

x21 = -29.3972978121741

x22 = 56.5486676615182

x23 = 0.0

x24 = -46.0009258739809

x25 = -24.0097772988524

x26 = 83.7000377170584

x27 = 70.2380023088414

x28 = 84.8230016455603

x29 = 94.2477796093532

x30 = -13.6893345442251

x31 = 72.2566310277262

x32 = 19.9725198514047

x33 = -61.7088891419299

x34 = 15.707963375677

x35 = -49.1425185275707

x36 = -97.3893723324611

x37 = 65.973445752458

x38 = 100.530964809623

x39 = 81.6814090930582

x40 = 78.5398162353179

x41 = -6.28318528499201

x42 = -57.6716316944822

x43 = 59.690260521201

x44 = -87.9645943595892

x45 = 74.2752597562891

x46 = 30.292962606032

x47 = -19.9725198514047

x48 = 15.7079633325005

x49 = -72.2566309208634

x50 = 92.22915088397

x51 = 93.1248156778278

x52 = -75.3982237654215

x53 = -31.4159263611514

x54 = -81.6814090368274

x55 = -15.7079632961432

x56 = 6.28318528447673

x57 = 85.9459655767904

x58 = 37.6991119487137

x59 = 21.9911485851464

x60 = 12.5663705157251

x61 = -59.6902604567849

x62 = 41.9636684265333

x63 = 52.2841111811605

x64 = 4.26455658345576

x65 = -89.983223024238

x66 = 28.2743338653149

x67 = -37.6991118765599

x68 = 96.2664083314176

x69 = -21.9911485865029

x70 = -2.01862872372383

x71 = 34.5575190882925

x72 = -83.7000377170584

x73 = -67.9920744491095

x74 = -2112.27322714221

x75 = 38.8220757729435

x76 = -39.7177405668013

x77 = 67.9920744491095

x78 = 48.2468537337129

x79 = -41.9636684265333

x80 = -50.2654823461522

x81 = -51.3884463873027

x82 = -6.28318519784509

x83 = 87.9645943349834

x84 = 24.0097772988524

x85 = -85.9459655767904

x86 = -94.2477794959085

x87 = -53.4070751968407

x88 = -92.22915088397

x88 = -92.22915088397

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Expresiones idénticas

Expresiones semejantes

4cos4x-3cos2x-1=0 la ecuación

Solución numérica:

Solución