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

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
   4           4/      pi\      
cos (3*x) + cos |3*x - --| = 1/4
                \      4 /      
$$\cos^{4}{\left(3 x \right)} + \cos^{4}{\left(3 x - \frac{\pi}{4} \right)} = \frac{1}{4}$$
Gráfica
Suma y producto de raíces [src]
suma
  5*pi   pi   pi   pi   pi   5*pi
- ---- - -- - -- + -- + -- + ----
   6     2    6    6    2     6  
$$\left(\left(\left(\left(- \frac{5 \pi}{6} - \frac{\pi}{2}\right) - \frac{\pi}{6}\right) + \frac{\pi}{6}\right) + \frac{\pi}{2}\right) + \frac{5 \pi}{6}$$
=
0
$$0$$
producto
-5*pi -pi  -pi  pi pi 5*pi
-----*----*----*--*--*----
  6    2    6   6  2   6  
$$\frac{5 \pi}{6} \frac{\pi}{2} \frac{\pi}{6} \cdot - \frac{\pi}{6} \cdot - \frac{5 \pi}{6} \left(- \frac{\pi}{2}\right)$$
=
      6
-25*pi 
-------
  5184 
$$- \frac{25 \pi^{6}}{5184}$$
-25*pi^6/5184
Respuesta rápida [src]
     -5*pi
x1 = -----
       6  
$$x_{1} = - \frac{5 \pi}{6}$$
     -pi 
x2 = ----
      2  
$$x_{2} = - \frac{\pi}{2}$$
     -pi 
x3 = ----
      6  
$$x_{3} = - \frac{\pi}{6}$$
     pi
x4 = --
     6 
$$x_{4} = \frac{\pi}{6}$$
     pi
x5 = --
     2 
$$x_{5} = \frac{\pi}{2}$$
     5*pi
x6 = ----
      6  
$$x_{6} = \frac{5 \pi}{6}$$
x6 = 5*pi/6
Respuesta numérica [src]
x1 = 56.2868683768171
x2 = -66.2352451131848
x3 = 40.317105721069
x4 = -34.8193185772869
x5 = 25.9181393921158
x6 = -5.75958653158129
x7 = -15.9697626557481
x8 = -97.9129710368819
x9 = -62.0464549083984
x10 = 47.6474885794452
x11 = -95.8185759344887
x12 = -84.037603483527
x13 = -49.7418836818384
x14 = -1.30899693899575
x15 = -23.3001455141243
x16 = -81.9432083811338
x17 = 20.4203522483337
x18 = 74.0892267471593
x19 = 91.8915851175014
x20 = -13.8753675533549
x21 = 67.5442420521806
x22 = 36.1283155162826
x23 = 58.1194640914112
x24 = -29.845130209103
x25 = 32.2013246992954
x26 = 100.269165527074
x27 = 3.92699081698724
x28 = 16.2315620435473
x29 = 76.1836218495525
x30 = -64.1408500107916
x31 = -59.9520598060052
x32 = -37.9609112308767
x33 = 89.5353906273091
x34 = -9.68657734856853
x35 = 60.2138591938044
x36 = 80.1106126665397
x37 = 78.2780169519457
x38 = 47.9092879672443
x39 = 82.2050077689329
x40 = 1.83259571459405
x41 = 45.553093477052
x42 = 96.0803753222878
x43 = -33.7721210260903
x44 = 71.9948316447661
x45 = 14.1371669411541
x46 = 84.2994028713261
x47 = 75.1364242983559
x48 = 12.30457122656
x49 = 28.012534494509
x50 = -67.5442420521806
x51 = 50.0036830696375
x52 = 42.4115008234622
x53 = -25.6563400043166
x54 = 6.02138591938044
x55 = -11.7809724509617
x56 = -79.8488132787406
x57 = 8.11578102177363
x58 = 739.845069920396
x59 = -40.0553063332699
x60 = 54.1924732744239
x61 = -3.66519142918809
x62 = 93.9859802198946
x63 = -20.1585528605345
x64 = -91.6297857297023
x65 = 38.2227106186758
x66 = -47.6474885794452
x67 = -121.998514714404
x68 = 34.2957198016886
x69 = -57.857664703612
x70 = -55.7632696012188
x71 = 52.0980781720307
x72 = -42.1497014356631
x73 = 30.1069295969022
x74 = -51.8362787842316
x75 = -99.7455667514759
x76 = 18.3259571459405
x77 = -18.0641577581413
x78 = -77.7544181763474
x79 = -73.8274273593601
x80 = 10.2101761241668
x81 = 98.174770424681
x82 = 86.3937979737193
x83 = 64.4026493985908
x84 = -45.2912940892529
x85 = 69.9004365423729
x86 = -35.8665161284835
x87 = -48.6946861306418
x88 = 62.3082542961976
x89 = -71.733032256967
x90 = -86.1319985859202
x91 = -69.6386371545737
x92 = -27.7507351067098
x93 = -93.7241808320955
x94 = -7.85398163397448
x94 = -7.85398163397448