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sqrt(1-cos(x)^2)=4cos(x)^3-3cos(x) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   _____________                       
  /        2            3              
\/  1 - cos (x)  = 4*cos (x) - 3*cos(x)
1cos2(x)=4cos3(x)3cos(x)\sqrt{1 - \cos^{2}{\left(x \right)}} = 4 \cos^{3}{\left(x \right)} - 3 \cos{\left(x \right)}
Gráfica
0-80-60-40-2020406080-1001002-2
Suma y producto de raíces [src]
suma
pi   5*pi   3*pi
-- + ---- + ----
8     8      4  
(π8+5π8)+3π4\left(\frac{\pi}{8} + \frac{5 \pi}{8}\right) + \frac{3 \pi}{4}
=
3*pi
----
 2  
3π2\frac{3 \pi}{2}
producto
pi 5*pi 3*pi
--*----*----
8   8    4  
3π4π85π8\frac{3 \pi}{4} \frac{\pi}{8} \frac{5 \pi}{8}
=
     3
15*pi 
------
 256  
15π3256\frac{15 \pi^{3}}{256}
15*pi^3/256
Respuesta rápida [src]
     pi
x1 = --
     8 
x1=π8x_{1} = \frac{\pi}{8}
     5*pi
x2 = ----
      8  
x2=5π8x_{2} = \frac{5 \pi}{8}
     3*pi
x3 = ----
      4  
x3=3π4x_{3} = \frac{3 \pi}{4}
x3 = 3*pi/4
Respuesta numérica [src]
x1 = -66.7588438887831
x2 = 532.107255701771
x3 = 52.2289778659303
x4 = 82.0741080750334
x5 = -27.4889357189107
x6 = 29.0597320457056
x7 = 44.3749962319558
x8 = 1.96349540849362
x9 = 33.7721210260903
x10 = -54.1924732744239
x11 = -49.872783375738
x12 = -71.4712328691678
x13 = -19.2422550032375
x14 = 79.717913584841
x15 = -52.2289778659303
x16 = 0.392699081698724
x17 = 96.2112750161874
x18 = -56.1559686829176
x19 = 42.0188017417635
x20 = 65.1880475619882
x21 = 21.2057504117311
x22 = 56.1559686829176
x23 = 93.8550805259951
x24 = -8.24668071567321
x25 = -100.138265833175
x26 = -12.1736715326604
x27 = -89.9280897090078
x28 = 12.1736715326604
x29 = -79.717913584841
x30 = 92.2842841992002
x31 = -87.5718952188155
x32 = 73.0420291959627
x33 = 77.7544181763474
x34 = 46.3384916404494
x35 = -96.2112750161874
x36 = 69.5077374606742
x37 = -5.89048622548086
x38 = 16.4933614313464
x39 = -3.92699081698724
x40 = -43.5895980685584
x41 = -69.5077374606742
x42 = -1.96349540849362
x43 = 48.3019870489431
x44 = 49.872783375738
x45 = -4408.43989114988
x46 = -35.7356164345839
x47 = -86.0010988920206
x48 = -98.174770424681
x49 = -82.0741080750334
x50 = -29.4524311274043
x51 = -73.4347282776614
x52 = 62.4391539900971
x53 = -93.8550805259951
x54 = 60.4756585816035
x55 = 8.24668071567321
x56 = 88.3572933822129
x57 = 54.1924732744239
x58 = 38.0918109247762
x59 = -47.9092879672443
x60 = -58.5121631731099
x61 = 35.7356164345839
x62 = -75.7909227678538
x63 = -10.6028752058656
x64 = -31.8086256175967
x65 = -38.0918109247762
x66 = 40.0553063332699
x67 = -84.037603483527
x68 = -10.2101761241668
x69 = -91.8915851175014
x70 = -25.5254403104171
x71 = 18.45685683984
x72 = 14.5298660228528
x73 = -60.4756585816035
x74 = 3.92699081698724
x75 = -42.0188017417635
x76 = 86.0010988920206
x77 = -63.2245521534946
x78 = -45.9457925587507
x79 = -77.7544181763474
x80 = 5.89048622548086
x81 = -157.472331761188
x82 = 75.7909227678538
x83 = 68.7223392972767
x84 = 31.8086256175967
x85 = 98.174770424681
x86 = -40.0553063332699
x87 = 100.138265833175
x88 = 58.5121631731099
x89 = -33.7721210260903
x90 = 10.2101761241668
x91 = -22.776546738526
x92 = 84.037603483527
x92 = 84.037603483527